Are you on public transport? If so, you're kind of screwed.
The Whole Foods in Glover Park, just north of Georgetown, doesn't strike me as as bad as you seem to have found it. Hunt up the dry-aged prime beef. The fish there can be pretty good, as well, and the cheese selection. Get the wine across the street at Pierson's.
When I go looking for meat, if I'm not at the Whole Foods I'm at Union Meats in Wienoo's new stomping grounds of Eastern Market. Bought an excellent prime rib there for Thanksgiving. There's also a passable cheese shop and, if you want to cook all nose-to-tail, you can get more obscure bits of pork. The fishmonger there is to be avoided at all costs.
The Dean & DeLuca in Georgetown generally has a very limited fish and meat selection and it's pricey, but it's usually damn good.
My thought for the best fish in town is the market at Black Salt
, which isn't exactly around the corner but is probably only three turns from Wisconsin Avenue (where I assume you're staying). Best fish market I've ever seen not in Crete. Also, it's next to a no-longer-brilliant-but-still-passable bakery and one of the best wine stores in town.
I've never been a huge fan of Wagshal's butcher shop, but in deference to the many whom I respect and who are indeed big fans, and to the fact that the directions are brutally simple -- "go down Wisconsin to Massachusetts and take a right(west) and go to the District line" -- I include it
Finally, assuming that you're staying in Cathedral/Cleveland Park, the best Indian Restaurant (Heritage of India) and the best strip club (Good Guys) are across the street from one another, just down the hill from Wisconsin Avenue. Just sayin'.