I just went with 2 adults, 2 kids (7 and 8) a few weeks ago for 3 nights. 3 nights is NOT enough time, but neither would be a week - to see everything. So we went for 3 nights this time and have a list of things to see next time already!
My budget ended up a bit higher than I had planned. It SEEMS like it should be so inexpensive because admission is free to most/all places, but the costs add up. This is my approximates:
Hotel for 3 nights (parking was included): $375 (Marriott Wardman Park - HIGHLY recommend it, great area (not scary), right next to Metro and walking distance to zoo
Dinner at hotel on arrival day (kids eat free) = $70 (but we had leftovers for part of another meal)
Metro passes 1 day: 4 x $5 = $20
IMAX theater show at Air & Space = 4 x 8 (not sure of price, but think this is it) = $32
Food on Mall day - lunch = about $30
ice cream on mall day (much needed rest) = about $15
dinner (there are a bunch of restaurants right next to our hotel - got 'to go' on way back to room 2 nights) night 1 = about $30
Zoo - free and we brought our lunch in a cooler (worked out great) - but we bought some souveniers plus pretzel and popcorn here so likely spent about $50.
Dinner on 3rd night - used leftovers but bought some too = about $20
Monuments by Moonlight tour - highly recommend it as everyone's legs were very tired and honestly we wouldn't have seen nearly as much if we hadn't spent this $$ - ours came right to our hotel to pick up/drop off total = $120
Gas from upstate NY = about $70
Total = $832
More than I thought I would spend, but still reasonable.
Good luck!
Oh and BTW it rained the entire day we walked around the mall. Bring ponchos and good shoes (maybe
crocs?) - my son's socks were wet all afternoon and he kept wanting to go change his socks.