Miraflores

For a bit of fun in Miraflores, try the small street between Parque Kennedy and Bellavista, locally known as the "calle de las pizzas" (Pizza Street). It is a big tourist trap, but on the other hand you are guaranteed to meet other travelers in high spirit.
At the end of Av. Larco you can find the LarcoMar amusement area, with spectacular views of the beaches, about 40 meters below it, and the Pacific Ocean, and the usual western style shopping mall shops and fast food chains.
Crypto, heavy metal and hard rock pub on the first side-street of Calle de las Pizzas. Unmarked entrance, just a black door. They sell pitchers of rum & coke for about $5. Excellent atmosphere if you're in the scene, but a bit intimidating for tourists who just wander in.
Café de la Paz is another excellent choice, right in front of the Kennedy Park. Peruvian-french food, very trendy and a bohemian atmosphere. Excellent Pisco Sour.
Nebula, Gonzalez Prada 194 (between cuadra 50 and 51 of Av. Arequipa), Miraflores, is a disco with music from the darker part of the eighties, quite close to Plaza Kennedy.
For jazz music, Miraflores holds a couple of good options: Jazz Zone, Avenida La Paz 656, and Satchmo.
And for all the coffee-addicts, there are a number of good options. Try Il Cappucino, a new cafe in Miraflores. Manuel Bonilla 103, close to Parque Kennedy. Also close to the Parque are Café Z, about a block down Bajada Balta; and La Máquina, on the corner of Diez Canseco and Alcanfores, also about a block from the Parque. Excellent coffee is also to be found a few blocks farther away at Arabica Espresso Bar on Calle Recavarren.

Barranco

Barranco is a neighborhood south of Miraflores with many clubs and cafes, popular among college students in Lima. It's the party heart of town, where you can find most Peñas, music clubs that offer folkloric music shows, in particular Afro Peruvian and Criollo gigs. On the weekends, Barranco has "A Taste of Barranco" food festival. Outdoor tables are filled with every dish they serve, the price is very reasonable too. Local musicians play and it's a very popular place to be. For live music, Barranco is also good. Some of the best clubs for rock music include 6 places within a few blocks:

La Noche, Avenida Bolognesi 307, usually offers live rock, but on Monday night they have live jazz.
Mochileros is a popular hang-out for backpackers, with a nice and cozy basement. It is also a hostel.
Sargento Pimienta (Sgt. Pepper) the biggest rock bar/club in town, long lines from Thurdays to Saturdays after 11PM.
Del Carajo if, besides dancing, you want to enjoy a good show of Peruvian music.
El Dragón A.K.A el Drogon. The place to be any Wednesday night of the year
El Tizon
Watdajel as in "what the hell".
Canta Rana - The Singing Frog - Get there early for lunch because it fills up with locals! Fresh scallops with the Peruvian version of Parmesan, wonderful.

City center

Around Plaza de Armas you can find some nice bars. Around Plaza San Martin you can find "El Directorio", "De Grot" and "Mao Bar", which are small rock pubs occasionally hosting shows from local bands and low-priced beer, when compared to similar places in Barranco or Miraflores.

Drinks

The Pisco Sour is the national drink of Peru, made with Pisco, a brandy made of grapes. It is highly recommended that all adult visitors to Peru try this drink at least once before exiting the country. Visitors might be amused to learn that a controversy exists between Peru and its neighbor Chile over whose country really created the Pisco Sour, although the Chilean and Peruvian recipes are somewhat different (Chilean people like to argue that Pisco is a Peruvian spirit while the Pisco Sour recipe comes from Chile, when in fact both the main ingredient and the drink were created in Peru). Variations include Maracuya Sour and Coca Sour and are offered in several bars around town.
People say if you don't drink Inca Kola at least once, you haven't been to Peru, the most popular drink in Peru, one of few sodas that Coca Cola couldn't defeat in the world (until they bought the company, a strategy employed more than once ). It's a yellow-fruit flavored drink that tastes like cream soda. Peruvians are really proud of it, so if your tourist guide offers it to you, accept it. They will be more than happy with your gesture. It's a very sweet soda, but drinkable mainly because it's not as gassy as Coca Cola. This makes it and ideal drink to join a plate of heavy or spicy food, like Chifa.
You can find great fresh fruit drinks all over Lima. Starting from 50 centavos for a fresh orange juice at the market to some more expensive ones. The surtidos, containing of several different fruits are quite tasty.