Local law prohibits serving alcohol after 4 AM. There are a number of speakeasies defying this.
(right inside a building about ten metres before the corner.).
Cafes
Alexander The Great, Av. 16 de Julio 1832 and other locations. Many thought the legendary Macedonian slayer had long since died. Not so infact, although he is considerably tamer after a rough encounter with a fiery cholita.
Blueberries, Av. 20 de Octubre 2475. This café serves very delicious coffee, and also has a very appealing breakfast menu. The café is situated at the east end of Plaza Avaroa, where you may also find an "Alexanders Coffee".
Pepe's Coffee Bar, Jimenez 894. Decent coffee and a nice calm getaway close to the tourist ghetto. Sandwiches are disappointingly small, but tasty. The "Trekker's Breakfast" is huge and delicious.
Bars
Blue Note Café/Wine Bar, Plaza gaston Velasco, Viluyo esq. Linares (1 block from sagarnaga and illampu; at the top of the stairs when you exit Oliver's). Great vibe; it's a fantastic place to chill with friends, have a drink & a bite to eat. The people behind the bar know their stuff (from martinis to wine to local beer), and there's excellent chili, lamb chops and tapas on the menu. Good prices compared with other bars in the area; it's open from the late afternoon onwards.
Oliver's Travels, Calle Murillo (opposite Sol y Luna) is a Northern English owned backpackers bar serving standard English fare at mid-range prices. Under new managment so doesn't have the problem of the (In)Famously obnoxious drunk in charge. Fun party atmosphere,and a warm welcome from Eglish speaking staff. Also has travel Has wi-fi and tv for most sporting events and a GREAT book exchange (best in South America - but expensive). Also has a great tour agency and great happy hour Sunday to Thursday. Wednesday Nights are Theme orientated with fancy dress. Also availabe for big bookings for tour groups. Also has great food, the breakfast is very nice and not too overpriced compared with the other local options.
Sol Y Luna, Calle Murillo, is a Dutch owned & managed traveller's hangout. Good atmosphere, different areas, live music, free wi-fi zone, television, large screen for important football games, and a Pool Table. Serves Coca Leaf Mojitos, where Coca leaves are substituted for mint leaves!
Irish, on Plaza Avoroa, pathetically named Irish themed bar. Food is overpriced but good, and the cocktails are reasonable, though behind the above mentioned bars. Mostly frequented by Bolivians and should be scorned by real Oirish people.
Traffic, in San Jorge is a bar with a good atmosphere and fairly good music. There is a large dance floor and a comfortable bar. Owner Asher has taken 6 steps back from managing the place after a sting operation codenamed 'superhuey' .
Antique Pub, at Pichincha 662 has recorded rock music, and all sorts of old things including fob watches, photographs, a kid's tricycle and a six shooter to keep you amused. They serve food too.
Pomp Pomp Salty Man, on Loayza and Comerceo. Known for its great clandestine happy sauces. ATM on premises.
Hard Rock Cafe, Calle santa-cruz #399 esq. illampu, ? 2119318. 10PM-4AM. Open all week long, great parties, all kind of music. The biggest bar in Bolivia serves almost every drink there is. Full with backpackers and locals, great music and atmosphere.  edit
Clubbing
Mongo's, Hermanos Manchego 2444. Since 1995 has remained one of the most popular places for travellers with a good mix of locals. It's a lively atmosphere every night of the week at this place. Open from 6:00 PM till 3:30 AM. Serving the best in global cuisine, and well priced. Be careful, though, as many tourists (as of July 2009) have reported being duped by being charged much higher prices for drinks than listed on the menu. Check your bill carefully!
Ram Jam Presbitero Medina 2124, near Plaza Avaroa , is another popular place, Less gringos than Mongos. Serves Saya beer from Adventurebrew hostel. Occasional live gigs. 0,6 l beer 18 Bs. Saturday cover charge 10 Bs.
Forum, Near Plaza Espana is a mostly Bolivian hangout. It is La Paz's one of two proper disco venue (the other one is called Soundbar). Upper class Bolivians frequent the establishment very dressed up. Worth a look if you're missing a big club with big pretensions.
La Gitana, Zona Sur, Calle 8 de Calacoto, is a bar/club hangout for upper class youth of La Paz's South Zone.
Dry Law, Zona Sur, Cota Cota, is a pretty hip club in La Paz's rich South Zone that's slightly on the right side of pretentious. Good alternative to Mongo's or RamJam if you're sick of bumping into Gringos all the time. Dress well.