"@Welcome, I just finished my tour of the Captiol and I'm hungry. However I don't want to pay $5 for a hot dog, and I want to sit down at a table. Where do I go?"
Thanks for the question, hypothetical reader. Just from spending time at the Mall, I'd say this is the single most question I get asked. (I usually have a dog with me, so I guess people just assume that I'm a local).
There are kiosks on the mall that sell food, as well as food carts, but you want to sit down. Here are some different options, depending on where on the mall you are.
1. (from the Capitol, south) Pennsylvania Avenue SE to/and Eastern Market
As you walk down Penn Ave, you will find a bevy of restaurants; mostly pubs. There is also Good Stuff Eatery and We The Pizza, Firehook, and Quiznos. Beyond that if you take a right on 8th st there are a ton more restaurants down that way (Eastern Market).
2. (from the Capitol, north) Union Station
As mentioned in a previous post, there's a lot of stuff at Union Station. This includes both sit down places (Uno's, Thunder Grill, etc.) as well as a food court.
The area around L'enfant plaza to me is the most confusing geographical area in DC. I get lost around there every time I walk. However, if you can make it to the plaza there is a food court with many options.
4. (7th st, north) Chinatown
DC's Chinatown, while it does have an above average number of Chinese restaurants, is more like... American restaurants and stores with Chinese letters on their signs. Clearly you can eat Chinese food here, but there are also a LOT of other places, from chains like Ruby Tuesdays to
Nando's Peri Peri (<-- highly recommend, though it is on the spicy side!).
5. (12th St, south) Not much.
6. (12th St, north) Aria
As you walk north on 12th St NW, you will enter the business district of DC. There are a ton of people that come into DC on a regular weekday, and all of them need lunch. Because of this there are a ton of delis/lunch spots. However, most of them will be closed on weekends or after hours. One restaurant that I've always had luck with (and is pretty cheap) is
Aria. It's pretty basic with pizza, paninis, and a few pasta dishes. But it's pretty good, cheap and open during weekends/off hours.
There is also a food court near Metro Center (around F and 13th NW). (Limited hours Saturday, closed Sunday).
7. (17th to 23rd st, north) Foggy Bottom
As you get above E st NW you get into Foggy Bottom/George Washington University territory. There's a TGI Fridays at 21st and Penn if you're looking for something familiar, otherwise walk around and eat what the college students eat.
That's about all the advice I have on that. Just remember that cost of living in DC is pretty high, so expect to spend at least $8-10 on lunch, even if you just go to a food court.