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In Arlington, Restaurant Three and Liberty Tavern are pretty good. Both serve new American cuisine and are located the Clarendon area.

In DC, Zaytinya (Mediterranean mezze) is a favorite; also Jaleo (Spanish tapas), owned by the same chef/owner. They are about two blocks apart in the Penn Quarter area.

PS - if you're looking for a nice DC restaurant, be sure to check out Hook in Georgetown. Sustainable seafood, cooked to perfection. A must try is the wood grilled calamari.

I second Tallula in Arlington - it is one of my favorite restaurants in the country!

Others have covered the more upscale choices of restaurant, but if you're looking for breakfast or lunch, or you're on a budget, here are some places you might want to check out...

There are two middle-eastern places in Arlington that I like that you might want to give a try: The first one is called Ravi Kebab, on the corners of Glebe and Pershing -- you'll probably need a car to get there. (There are two locations, kitty corner from each other.) My wife and I really like the boneless kebabs there. The other is called The Food Factory, which is across the street from the Ballston Metro (cross the street, and walk past the chinese restaurant on the corner -- turn right in the parking lot behind it, and the entrance is in there.)

I strongly suggest you try to hit a peruvian chicken place while you're here. There are several to choose from. I like El Pollo Rico on North Kenmore in Arlington. There's also Crisp and Juicy over on Lee Highway.

If you've been out partying late, late, and looking for a bite, there's Bob & Edith's on Columbia Pike, a local landmark that is open all night. The food isn't really that great, but adaquate, and it's been around forever, and is an ideal stop after the bars close.

If you'll be in town for the weekend, and have a car, head up to Seven Corners on Route 50 for a place called Fortune. Arguably, the best dim sum brunch in the area. It opens at 11, and gets crowded fast -- get there early to avoid the wait.

Although it's a national chain, Smoothie King makes a great, quick breakfast, too. There's one across the street from Ballston Mall, and there's another one near Pentagon City Mall, too, in Pentagon Row.

If you're midtown and looking for a fast, quick lunch, try Potbelly. There are a bunch of locations, all over, and they're better than Subway.

Finally, if you're going to be visiting the Smithsonian Museums, there's not a lot of choices to eat. None of them are high dining, but if you are hitting a bunch of the museums and don't want to take the time to leave the National Mall, these are your best choices... The best one is arguably the cafeteria at the Museum of the American Indian, on the Capitol side of the Mall. They offer a very diverse menu of authentic native american cuisine. There's a food court under the Ronald Reagan World Trade Center on 14th, but it's not much better than a shopping mall food court. There's another cafeteria in the National Gallery East Wing, but again, the food isn't all that great, nor inexpensive.

Hope this helps. Let us know where you went!

cooking monster

Most all of the restaurants that I mentioned are casual and inexpensive (i.e. perfect for teenagers). Not sure where you are staying in Arlington or whether you will have a car. Also not sure whether you'll be close to the museums and monuments on the National Mall during the day. All of these factors will influence recommendations.

I second all the Arlington recommendations made by DaveFaris - especially Ravi Kebob and El Pollo Rico (though both require a car). Also, the cafeteria at the Museum of the American Indian is definitely the place to eat on the mall.

When I was in high school, my friends and I ate at Cactus Cantina and 2Amys (listed above) at least once a week, and our other favorite spots were Teaism (several locations around the city), Malaysia Kopitiam (in Dupont Circle), Zed's, and Aditya (also, both listed above). Another more upscale place I forgot to mention is Agraria in Georgetown, a fun restaurant owned by South Dakotan famers, that uses only local ingredients (well, I think the beef is from the South Dakota farms, but I think that's the only exception). My brother would have me recommend Rockland's barbeque to you as well, although I'm a vegetarian and haven't eaten there in years (its on Wisconsin Avenue in upper georgetown. There's a great ice cream place called Max's Best next door...my picture has been a part of his massive photo wall collage since I was 6)
The Jaleo in Penn Quarter is very good, but I've never been to the other locations. Zaytinya is, as someone mentioned, owned by the same group, and it is probably my favorite of the two (although I guess it depends if you're in the mood for tapas or mezze).
If you're looking to eat on the mall, my recommendation would be to either buy or make sandwiches to bring with you. Good sandwich places include Firehook bakery, Marvelous Market, Booeymonger's, all of which have several locations around the DC area. Then, when you're craving some dessert, stop by the lower level of the National Gallery for some gelato!

I echo the 2 Amys recommendation. Be prepared to wait for a table, though!

Jaleo has been variable on my last few visits. I would probably recommend it for lunch instead of dinner; it always seems too crowded at dinner time and I feel like I'm being rushed to finish the meal, which is definitely not how tapas should be.

Recently had an excellent brunch at Farrah Olivia in Old Town Alexandria. It's a nice atmosphere, and the food was great. They don't show them on the website, but they offer prix fixe options for brunch and for pre-theater (early dinner). These are fabulous deals, because they are essentially combinations of items on the menu. I had a three-course brunch for $20--filling and delicious. May be a good place to fuel up before hitting the museums, though I don't think they open until 11 or so.

An easy (and fun) excursion from the Mall is also Eastern Market (accessible by Metro from Smithsonian stop). Market Lunch is a great stop for breakfast (Blue Buck Pancakes!!) and for lunch. And there are craft markets around that teenagers might enjoy.

For a nice sit-down meal in Arlington, I'd highly recommend Willow Restaurant. Chefs Tracy O'Grady and Kate Jansen offer a wonderful selection of food. It's just a short metor ride from Clarendon -- 2 stops, I think. http://www.willowva.com

In DC, I'd second the suggestion for Palena. Take the metro to Cleveland Park and, as recommended, sit in the cafe section (unfortunately there's no reservations taken). The food is always a hit.

Brasserie Beck and Central are two restaurants that you can't go wrong at. Central's Michele Richard is all the talk these days (his flagship restaurant received #1 in DC), but I actually prefer Brasserie Beck.

2Amys is a fun little pizza joint, but expect a wait.

Here is a classic, literate and very nasty review of Rosa Mexicano:
http://forums.egullet.org/index.php?showtopic=35847&mode=threaded

Regarding Agraria: The motives cited by the lobby of farmers from North Dakota in wishing to promote local food in Washington, D.C.--versus the food of farmers who travel from nearby VA, MD, PA & West Virginia which many established restaurants already feature--seemed rather disingenuous from the beginning. Cf. Michael Pollan on the Farm Bill, etc., to understand what stake wheat farmers from the state might have in maintaining a visible presence in our nation's capital, and why it might take the form of a lovely salad of fresh greens as opposed to a box of cereal. At any rate, Agraria's operations are marked by chaos: departing chefs, abrupt change in menus, and predictions of doom. Look for grim reports in The New York Times. Views of local diners interacting with one of the investors below, where you'll note, some initial, happy reports are followed by lots of recent, severe criticism.
http://www.donrockwell.com/index.php?showtopic=1742

As for pizza, 2Amys is great, but you need to put up with lots and lots of screaming young children. Look into Comet Ping-Ping for a fairly new, highly praised pizza joint by one of D.C.'s most respected chefs, Carole Greenwood. The two have surpassed Pizza Paradiso which used to better.