DAR is right by the white house and monuments, so there isn't anything immediately around there... might be somwthing in foggy bottom, 10 minute walk. probably an easier bet is K street, the is a McCormick & Schmick's for seafood (sp?) at 15th/16th, and Morton's on Conn for steaks (both fancy and on the pricey side). if you want something original you might have to go up to Dupont or Georgetown.
closest place to DAR for a drink is in the basement of the chi-chi hotel at 16th & H, north side of lafayette park. they have above-average pub grub, definitely enough for a decent meal. it's oak-panelled and looks fancy, but they'll serve anyone as long as you're not in ripped jeans.
oh, and i don't think DAR is such a terrible place to catch a show. sound has always been acceptable for me, then again i've never sat at the back of the hall - maybe the sound truly is horrible there.