Eat

Boulevard Lavaud, Compañía de Jesús 2789 (Cumming underground station), ? +56 2 6825243. M-Th 10AM-1AM, F-Sa 10AM-3AM, Su 11AM-5PM (from 31st October 2010). In Barrio Yungay, Boulevard Lavaud is more than a coffee and restaurant, is part of Santiago history. Better known as La Peluqueria Francesa, is part restaurant, part antique store and part hair salon Ch$1000-7000. 
Amadeus, Av. General Bustamante 50 (Between Buquedano and Parque Bustamante metro stations). Tasty wood fired pizzas that start at Ch$3500-4000. 
Anakena, Av. Kennedy 4601 (in the Hyatt Regency Hotel), ? +56 2 3633177. Designed to look like an outdoor market with a number of dishes that combine Asian, European and South American cooking styles. 
Aquí Está Coco, La Concepción 236 (Providencia), ? +56 2 2358649. M-Sa 1PM-3PM and 8PM-11PM. Seafood is this restaurant's specialty and its menu has a wide variety of fish and shellfish to choose from. There are a number of other dishes for the non-seafood lover as well. Currently under renovations following a fire, will reopen sometime in January. 
Bar Nacional (Matias Cousiño 54), Paseo Huérfanos 1151, ? +56 2 6965986. Offers hearty Chilean meals and a range of local and imported drinks. 
Café Dante, Jorge Washington 10 (Ñuñoa). A meeting point for friends, with a lot of history and nice service. 
Plaza Café, Av. Brasil 221 (Barrio Brasil). Pleasant place to eat a cheap three course lunch. 
Ocean Pacific, Ricardo Cumming 221 (Barrio Brasil), ? +56 2 6972413. Stylishly blue decorated restaurant that has a broad range of seafood. The take-away parlor next door with the same name, has excellent empanadas. 
Santa Isabel, Ricardo Cumming and Compañia (Barrio Brasil). Big supermarket where you can gather the ingredients for your own meal. It also has simple take-away items such as chicken or rice. 
Los Buenos Muchachos, Avda. Ricardo Cumming 1031, ? +56 2 698 0112. 12.30 PM - 01.30 AM. great food and great entertainment, what more does one need for a succesfull restaurant dinner. 
Ciudad Vieja, Constitución 92, Providencia, ? +56 2 2489412. Mon 12:30-18:30, Tue 12:30-00:00, Wed 12:30-01:00, Thu/Sat 12:30-01:30. A great "sanguchería", where you can have some of the most gourmet sandwiches in the city. Its located in the hip Bario Bellavista, and you can also have a drink with friends at very economical prices. 

Drink

Nightlife choices vary widely across the city and their location usually reflects their price and style.
Barrio Bellavista and Barrio Brasil are popular spots close to the city center. Bellavista can be reached by Metro to Baquedano, or by bus to Plaza Italia. Cross the bridge will bring you to Pio Nono, which probably has highest density of bars in Chile. Bellavista has a wide range of choices from popular places to upscale, such as a jazz bar. In addition, there are discos with all kinds of music, from contemporary eletro-pop to salsa and merengue. This is probably the only barrio where you can find a disco that has a predominately gay audience. It is a fun atmosphere and features drag-queen shows during Saturday nights. Moreover, Bellavista is the area that lasts the longest during Friday and Saturday nights, with most places closing at 4-5 AM, and a few places (so called "after hours") run till 6-7AM.
Plaza San Enrique is a park located in Lo Barnechea (at the far north-east of the city) which is sorrounded by nightclubs. Most popular one is Sala Murano (it can get very crowded!). People who attend are mostly 18-25 and it is one of the safest places to party. Most people there are from upper-middle to high class, so it is more expensive than other neighbourhoods. Typically, females get in for free, while males pay around 3k-5k CLP. You can get there by micro, but though buses do pass later on, you might have to wait up to an hour for it.
Boomerang, General Holley 2285 (Providencia). High scale pub and cocktail bar.  edit
La Casa Club, Santa Filomena 11 (Providencia), ? +56 2 7350503. Five level club with each floor catering to different musical tastes, laser show, bar and special events, highly recommended. 
Barrio Manuel Montt has a small and unique atmosphere with mid-range prices. It can be reached at Metro Manuel Montt (line 1).
Isidora Goyenechea is a very nice and safe neighbourhood with plenty of restaurants, albeit expensive ones. Take the Metro to El Golf.
Plaza Ñuñoa is a district east of the central area and is another popular spot nightlife spot.
The Santiago Pub Crawl. . Your night is planned out for you so you don't have worry about where to go, you meet people from all over the world, cover a lot of ground and it's great value for your money. 10,000 pesos. 
Batuta, Jorge Washington 52 (Plaza Ñuñoa), ? +56 2 2747096. A good spot to see mainstream Chilean rock and metal bands, although it is expensive by Chilean standards. 
Suecia is roughly located at Providencia and Suecia, in between Metro Tobalaba and Los Leones (line 1). It is a boulevard of bars and discos about 3 blocks long. It used to cater to a foreign and upscale audience, but it seems now that the most entertaining bars moved to Manuel Montt.
Vitacura is located pretty far east (towards the Andes). It is composed of bars and some places where you can dance. The places are nice and although they certainly lack cohesiveness as nightlife (since bars only recently started opening there) it can be fun to go. It is more expensive that other areas of Santiago and frequented by people that live in the eastern (wealthier) side of the city. Although you can get there by bus, it will be hard to leave on anything but a taxi since buses don't run late.
Bar Catedral, Merced 395. Nice bar downtown between between lounge bar and more folklorica. Good rock bands often come to play. 
El Candil, Providencia 1421 (metro Manuel Montt). til midnight. A quiet bar/restaurant in Providencia. The traffic outside is noticeable but not excessive and drinking outside here has a genuinely pleasant urban flavour. If you fancy making a night of it, Bar Liguria is practically next door. 
Pio Nono. til 5AM. Pio Nono in Bella Vista has an intense feeling, bars line the street on either side. The area has a very youthful quality but older visitors shouldn't be intimidated. One of the most lively areas of the city at the weekend.
Bar Liguria, Av Providencia 1373 (metro Manuel Montt). This bar looks like a 1950's American diner and plays music ranging from classic 1950s rock to what you'd hear in a mid-2000's London pub. For all that, it's clearly no tourist trap and the clientele are mainly local. At the weekend the bars on Pio Nono are probably a better bet, but for a mid-week drink this is well worth a visit. It is also a great restaurant during the day! It serves many local dishes and drinks, including great wines. 
La Leyenda, Alameda con Santa Rosa (metro Santa Lucia). til 5AM. This Peruvian restaurant/bar plays music from all over Latin America at weekends until 5AM to a diverse crowd of locals with roots all over South America. Unpretentious and entertaining. CLP3000/litre Heineken.