Max's is great.
Brickskellar is overrated; 20 years ago it was a breath of fresh air, but there are better places around now (especially since they're invariably out of the first 5-6 things you order; the 400+ beer list seems to be a list of everything they've ever had, not what's currently available).
Churchkey is probably the best place for beer in DC at the moment: http://www.churchkeydc.com/
has the draft list, they also have a ton of bottles. (the downstairs restaurant, Birch and Barley, does a great brunch).
The beer director for Churchkey (Greg Engert) also does the buying for Rustico in Alexandria ( http://www.rusticorestaurant.com/menus/menus.html
) but Churchkey is better if you only try one. If do find yourself in Alexandria, Bilbo Baggins also merits a visit: http://www.bilbobaggins.net/beer.html
though the food and table service are spotty. Sit at the bar.
If you're staying in Bethesda, you're very close to an awesome beer/wine/liquore store: http://www.chevychasewine.com/
RFD Drafthouse in DC is run by the Brickskellar owners and probably merits a visit: http://www.lovethebeer.com/rfd.html
A couple of outside-the-box ideas:
Pizzaria Paradiso in DC has a surprisingly decent beer selection for a pizza joint, and they sometimes have hard to find bottles socked away (form a rapport and ask what they have): http://www.eatyourpizza.com/menu/birre/
They also have great pizza (but see below).
Lost Dog Cafe in Arlington has quite a good sandwich/wrap selection in a laid-back location, and they have a pretty decent beer list: http://www.lostdogcafe.com/beer.htm
There's a 3 beer limit to drink on premises, but they sell everything to go in 6 packs--it's a good place to go, try 3 things with dinner to see if you like them, and grab them in bulk if you do.
2Amys is great food--probably the best pizza in the region (Paradiso and Comet Ping Pong are the 2 primary competitors). Their selection is small (maybe 6-8 taps and 10-20 bottles) but very deliberately chosen to pair with the food; you'll find Moretti on tap, but they also have a rotating selection of little-known Italian microbrews in bottles. And the pizza is otherworldly. http://www.2amyspizza.com/
Some must-visits for eating even if you're on a budget:
For great food in a reasonable price range with a casual atmosphere, Food Matters in Alexandria is awesome. Very small beer selection, but there'll be something decent (Bell's Two Hearted is usually one of the 6 or so options). http://www.foodmattersva.com/menu.asp
Thai Xing http://www.thaix-ing.com/
is basically a chef's choice Thai place. Make reservations. You'll leave happy.
Ray's the Steaks and Ray's Hell Burger are reasonably cheap (especially the latter) and totally awesome; both have a few decent craft brews as well as an extensive wine list.
If you're not on a budget, try to get in to Cafe Atlantico's tasting room, and eat at Central.