Barantic
Let's just say that if you're a beer lover, that should be the place where to go. It has 18 draught beers with local and Belgian beers. You can also discover some saucisson dried sausage. The best moment is during the afternoon, under the sun, in the middle of crowded terrasses, with your favorite beer and your saucisson. Enjoy the moment.
Couleur Café
Specialized in cocktails in the World Guinness Book of records with above 2,000 types and rhum.
Funky Munky
A cool vodka/cocktail bar located near an entrance for the Thabor park. Drinks are relatively cheap - the more you buy, the cheaper it gets. The bar serves 30 flavors of vodka, numerous cocktails including a Long Island Iced Tea, Cosmos, Sex on the Beach, and a delicious drink called a Purple Turtle, and a few beers on tap or in bottles. The bar hosts a poetry slam every 1st and 3rd Tuesday of every month, and a quiz night every Monday from about 8pm on. The bartender and owner! speaks both French AND English, so don't worry about having to speak perfect French.
Haricot Rouge
On a street north of the Place de la République, with a smoother feeling, serving hot chocolate and having board games.
Westport Inn
Another Irish pub. It's smaller, but it's got an authentic feel to it, and the drinks are slightly cheaper than at O'Connell's. It's just down the street from Place des Lices. But, according to the sign on the window, you're not allowed to bring in nuclear weapons, so if you're packing, go elsewhere :)
Mondo Bizarro is the punkrock place to be :)
Jardin moderne
Mostly a music hall, not a bar
Le Sablier
A bar famous for the concerts there at a time, it is also an excellent place to have lunch.
O'Connell's Irish Pub
Very popular Irish pub. Ask anyone and I'm sure someone will point you in the right direction. St. Patrick's Day at this place is insane - the pub becomes packed to capacity. Same rules apply for any big sporting events. Monday nights from 7pm-11pm and Thursday nights from 7pm-close are happy hour. A pint of beer/stout/ale is 4 Euros and in some cases, less during happy hour - just check the little posters up on the walls at the bar or ask the bartenders, they're all very friendly and most, if not all, of them are anglophones. Not only do the anglophones love this place, but the French do too.
night bars
Those are bars that have an extended closing time of 3am. There are bouncers for some of them.