You won’t need to take the metro, there are hundreds of restaurants within walking distance of 22nd and M streets, where you’re staying. Dupont Circle, Georgetown, and Adams-Morgan are all close by.
If you have the time, you might go for a walk first, just up M Street (as far as 34th), and see pretty much most of what Georgetown has to offer, and then back in the other direction.
If you’re interested in a real exploratory experience, take New Hampshire Avenue up to Dupont Circle (about 3-4 blocks), then up Connecticut Avenue, go another 3-4 blocks to Columbia Road. Another 5-6 blocks down Columbia Road is the Adams-Morgan neighbourhood (centered on 18th Street) and there is another ton of good restaurants there (besides the popular Madam’s Organ). My favorites in Adams-Morgan are Fasika (Ethiopian) and The Diner (a very reasonably priced place - clean, great food), but there are dozens of places to try and most will be well within your price range.
Last time I went to Meiwah (a couple of months ago), I did not enjoy the food.
There’s a very nice sushi bar within walking distance – Uni on P Street.
In Dupont Circle, there’s a nice Asian fusion tea room called Teaism (besides the tea, they have very good food). There’s another fusion place, Raku, next to Kramerbooks. (And there’s Kramerbooks’s own cafe, Afterwords). I haven’t been to Raku a while, though, so I don’t know whether it’s still good.
You’re also not far from Georgetown. If you want to take a longer walk (or a cab), one of the best Thai restaurants I’ve ever been to is **Busara **on Wisconsin Avenue. Another nice tea room on Wisconsin – Ching Ching Cha – this one’s more traditional than Teaism.
There’s a good Ethiopian restaurant in Georgetown – Zed’s – they have vegetarian platters too. That one is definitely walkable from 22nd Street. (I walk to that area from 25th Street often)
For even more casual, you can go to La Madeline, a French bistro in Georgetown (near the Barnes and Noble).
Eastward on M Street, away from Georgetown, you’ll find another row of restaurants and there are some popular ones there.
You’re also close to K Street just north of the White House, which has a lot of famous and popular restaurants.