Thanks people, that is really very helpful information. I'll try and Priceline something, probably in Whitehouse or Capitol Hill. I'll be staying a Saturday night and I read in another post that it's fairly easy to get a nice 4* hotel for a decent price.
(why doesn't Priceline have 5* hotels in DC? Or at least, they are not listed on biddingfortravel.com).

It'll be great!