If you don't have a car, it's difficult to get to any of these (except Passage to India, which is not a far walk from the Bethesda metro). For very good restaurants in DC, I would recommend Curry Club (upper Georgetown) or Jyoti (Adams Morgan) for Indian. Heritage India (Glover Park) is good as well. Good but upscale Thai at Rice on 14th Street and Simply Home on U. No good Korean or Vietnamese in DC. Chinatown Express (despite its name) has great Chinese noodles (Gallery Place/Chinatown). If you've never had Ethiopian, DC specializes in it - you can search the board for the best. Enjoy!
For greatness, travel you must. The best Asian food tends to be in the deep suburbs.
Here is a list. Do a search on Chowhound for specific recommendations.
Sichuan - Joe's Noodle House, Rockville, MD
Taiwanese - Bob's Noodle 66 in Rockville, MD
Dim Sum anytime - A & J, Rockville, MD or Annandale, VA
Ruan Thai, Silver Spring, MD
Myanmar, Falls Church, VA
South Indian vegetarian - Woodlands, Langley Park, MD (go for dinner. avoid the buffet-only lunch)
Indian - Passage to India, Bethesda, MD
Vietnamese - Eden Center, Falls Church, VA (a Vietnamese Shopping Center with about 23 Vietnamese restaurants plus bakeries, sandwich shops, etc)
Korean - Gom Ba Woo, Annandale, VA
Pakistani - Shiney's, Annandale, VA
Hong Kong - Full Kee, Washington, DC