DC is home to a large ethnic and international population, with a metropolitan population of over 5 million, even though the population of DC itself is about 600,000. There are tons of restaurants, from expensive to cheap, likewise for bars. Some of the best values are ethnic restaurants including Vietnamese (mostly VA), Thai (mostly VA), Indian, ... Metro Rail, Bus, and Taxi are easy and affordable so it's worth exploring.
Some good sites to find out about restaurants include:
Great Anywhere/Anything guides
In DC, VA, and MD, the drinking age is 21 for beer, wine, and liquor (spirits, alcohol). Almost all places will ask you to present a valid picture ID that has your birth date on it before purchasing alcohol or entering a bar. Bring your driver's license or passport with you when you go out!
Most places with waitstaff and bartenders expect a tip, typically about 15% of the total price. The staff get paid a sub-minimum wage and this is how they make their income; be generous if you get good service.
Beware that some places may add an automatic tip (gratuity) for parties larger than 6 people; this is so their staff don't get stiffed by a large party. Usually the bill or menu will state this but if in doubt, ask.
Price and Taxes
Typically, prices posted -- including menus -- do not include local taxes. These taxes vary by jurisdiction; in the downtown area of DC, expect to see 10% added to your bill in taxes; in Virginia, expect 5%.
Most places take credit cards, though some of the smaller "mom and pop" ethnic restaurants or small shops may only take cash. Cash machines (ATMs) are all over the place but most charge a fee ranging from $2 to $5 per withdrawal.
DC recently banned smoking in bars and restaurants. Virginia (a tobacco-growing state) has not, so many bars and restaurants permit it inside, though some do not. The closest Maryland county, Montgomery, has also banned smoking. Many buildings will have restrictions on how close to the door you can be while smoking. Check for posted signs regarding designated smoking areas when in doubt.
In DC, bars typically stay open until 1:30 on weekdays, and 2:30 on weekends. In VA, they're typically open until 1:30 a.m. all week.
Restaurant kitchens usually close about 10:00pm at night (22:00).