You will probably not find a place that just serves coffee and tea.  Most places serve at least beer and wine along with those things.  A few places are more geared towards drinking a non-alcoholic beverage than others, but there is no clear distinction.  

Saga

Piata Muzeului

This is a very nice place in Piata Muzeul.  In the winter you can go inside and enjoy a wide selection of teas and coffee prepared in a variety of ways.  In more temperate weather I would suggest taking a seat outside on the large patio.  Inside there is a room with a pool table in relatively good condition.  The interior is very nicely decorated with paintings of a vaguely eastern motif on the tables and on the walls.  The lighting is dim and the music is at a reasonable level so you can carry on a conversation.  The downside is the prices are not very Romanian.  The upside which trumps it all is that they serve Leffe Brun, a dark Belgian beer, which is very difficult to come by in America.

Insomnia

Str. Universitati 2

Insomnia moved to a new location in the summer of 2006, but you will still find the same art student crowd lounging about on bean bag chairs and sipping a coffee or having a beer.  You can get coffee, tea, or juice here, but most people are drinking beer.  The prices are moderate, but the atmosphere is very nice if you like art and the art world.  You can usually find an exhibition taking place in the café or just next door.  This is one of the few places you will find decent music playing, something different from the usual constant bass beat of bad European dance music.  I recommend it highly. 

Dorna

Piata Unirii 25

This is directly on Piata Unirii.  There are a few tables directly out on the sidewalk and it makes a great place to sit and watch the bustle of the square.  Teas and coffee are served as well as alcohol. 

Krakczar

Str. Vasile Goldis 2

Coffee, tea, and alcohol are served.  It is largely a hang-out for Hungarians, though Romanians are found there too.  This place earns the best music in any pub/café award from me.  I actually heard Tom Waits being played there.  It is a little dingy but the feel is good.  I haven’t been to this place at night, but apparently it is packed. 

Music Pub

5 Str. Horea

I have been to this place every time I visited Cluj.  It is one of the best places to see live music or to hear any music.  You can hear everything from Metal to Folk, Trance and 60’s rock here.  The crowd is young and most dress like they are going to a Nirvana concert, circa 1994.  It is very crowded during the school term and it is unlikely you will find a booth to sit in, though if you are an amiable type you will probably meet someone who will ask you to sit.  I have met several good friends there.  In the back you can find a small billiards parlor with five tables.  Just past the stage are two decent foosball tables that will cost you a 5000 lei coin to play on.  It is very smoky in Music Pub.  The bathroom costs a 1000 lei coin, which is annoying, and doesn’t help keep the bathroom clean, though there are two or three bulky solemn looking matrons positioned outside to collect your change and hand you a paper towel.  Music Pub is also one of the few places you will find Guinness which is a good thing, though you will pay four or five dollars for a pint.  You can go the other route and get a bottle of Skol for about 75 cents.  This place is good times and very crowded during the school year.  It usually stays open until about three.

Terasa Muzeu

Piata Unirii 17

One of my first memories of Cluj is having a Guinness in the open air courtyard of the art museum.  Recently, I caught a strange puppet show being performed in the courtyard.  You never know what you will find there, but it is one of my favorite spots to relax with a beer and talk.  It is very nice during the spring and summer though the beer garden is closed during the winter.  If you are interested in refreshments before seeing some art, or if you just feel like sitting outside, this is high on the list.

Ema Terasa

Str. Potaissa 14

This bar is just down from the Retro hostel and the best one you will find in this quarter. It is known to be a hang-out for artists and writers. Most people will not speak English in Ema, though. Standing in front of the Retro one night, a friend and I were invited to Ema by a man who spoke no English. We spoke no Romanian at the time either, but it didn't matter. He bought us a drink and somehow we talked, though I'm not sure what was actually communicated. The walls are painted with the visages of famous Romanian authors, painters, and poets. To my surprise before leaving that night, I found out the man who invited us for a drink was a famous painter from Cluj, whose face was on the wall.

Euphoria

Piata Muzeului

This bar/club is next to Saga.  The sound system is great, the music is bad.  It’s a place for the wealthier young people to dance on the weekends, and you will find them dancing on the tables, on the bars, and in every square inch of floor.  I’m not a dancer, but I thought I should mention this place for those who are.  Everything is more expensive here, but the clientele is attractive and young.

Billiard Club

Str. Bolyai Janos 12

This is one of the better places to shoot pool. I think they have a couple of snooker tables as well. The cues are decent and the tables are some of the best you will find in town. Most of the tables are in private rooms, so you can go there with a group of friends and not have to worry about bumping into people constantly, or crowds intefering with your shot. It is not very expensive, maybe three dollars an hour for the table, no matter how many players.

Jay’s Pub

Student Quarter

Large pub with the usual domestic Romanian beers available.  This is a very popular place with students.  It is something in between a pub and a club.  Dancing does happen but there is no dance floor.  I found myself standing around in a kind of circle with a bunch of people one night. As one person slowly started dancing others picked up.  I fled because I don’t dance.  The music is your standard Euro-dance stuff that makes my head want to explode, and the volume is very loud.  Walk inside and take a look around.  Not really my thing but you might enjoy it and you will probably meet some new friends.

30+

Avram Iancu 29

I don’t know where they got the name for this bar.  The clientele is of all ages but largely younger.  There is a large space for dancing and that does go on, but there are many tables to sit at and enjoy a drink also.  The best thing about this place is the music is run by a computer behind the bar, and it is wide ranging.  You will hear Guns ’N’ Roses and Whitney Houston, dance music and UB40.  I think the music is geared towards whatever people who are working there feel like listening too at the time, which is usually slightly better than the constant bass beat dance music you will hear in most places.  The mood is fairly relaxed and the prices are reasonable.  Not a bad place to check out if you get tired of the usual spots.

Elita

Student Quarter

Are you ready to rock?!!!!!!!!!  If you like death metal/heavy metal/black metal or just anything metallic then this is your watering hole.  Personally, my musical tastes rarely go there, but I have spent a couple of nights/early mornings in this cramped bar.  The beer is cheap, and beyond the skull t-shirts the clientele is largely friendly though very inebriated.  A guy slamdanced himself directly on top of our table spilling beer and shattering ashtrays one time.  He apologized, bought us beers, and ended up hanging out with us.  Not for the faint of heart, but if you are into this sort of thing, you should check it out and throw the goat.

Cafe Umbra de Noapte

Str. Georges Clemenceau 7

I'm not into the gothic scene but I actually like this place. I had some of the best coffee topped with ice cream here. The atmosphere and decor are certainly gothic. The walls are painted red and the lighting seems to intensify the color. A fair amount of dour looking Nine Inch Nail types moping about, but not much of the same attitude you would find in America amongst the same crowd. I went there as a joke and ended up actually liking it. If the goth scene is your thing then you will either like this place or find it slightly corny or probably both.

Nico

Student Quarter

Can’t say I like it.  This is one of several cramped student places directly next to the dorms.  The music is bad, but the beer is cheap.  Students like it because of the prices.  A policeman came in while I was there once and asked for identification from everyone, so I expect you will find a smattering of high schoolers trying to buy beer.  That is usually not a very difficult thing to do in Romania, and the drinking age is 18.  Don’t run away if someone asks you to go here, but don’t seek it out.

Club Caffe Florida

Str. Inocentiu Micu Klein 18

If you take my advice and stay at the Retro you will probably look at this place and be mildly tempted to enter.  I would suggest you don’t.  This is known as a Manele Club.  You can read about my take on Manale here. If Don Johnson suffered brain damage from falling off of a jet ski this is the kind of club he would open.  Pastel blues and pinks during the day, headache inducing lights at night.  Bad, bad, bad music.  Flee. Do not go.  I’m guessing the reason this place exists is because tourists staying at the Retro can be lazy or unadventurous and turn down the closest street for a drink.  Not suggested.

Pub Zone

Drunkenly wander around SE of Music Pub. You will find it.

So you need a beer and it is six in the morning.  Welcome to Pub Zone.  This is a non-stop bar.  That means something in Romania.  That means something everywhere actually and I can imagine if you know anything about the world of alcohol you can just about imagine the clientele.  The waitress is about 35, doing a decent job of pretending to be 20 and emitting a strange haze of intense sadness.  The clientele can be boisterous which is sometimes very good and sometimes very bad.  The entire place smells musty and the neon lights and revolving soundtrack of all the greatest hits from 1986 does not sound so good.  But if you need one more drink after the normal bars close Pub Zone is the place to be.  I’ve been there a couple of times and in some strange way it has a worn-out charm.  Can’t suggest it for most, but some of you have probably had experiences with bars like this elsewhere and if that is your thing, then head on over to Pub Zone, where the beer never stops flowing.

Cuba Libre

Str. Potaissa 6

This place is also right next-door to the Retro and that is where most of its clientele probably comes from. Not much to say about it, but that it has very comfortable chairs. The music is dance beat or hip-hop. The prices are a little geared towards tourists. Not a bad place for a final drink before going to sleep at the Retro. I don't know any Romanian who actually goes there, though I am sure several do.

Friends Club

Str. Emil Isac, across from Maimuta Plangatoare

Newer, clean bar across from the Crying Monkey. Music is the usual dance fare turned up too loud to actually talk to any of your friends. Nothing special there.