Washington D.C. (including Baltimore) - Where to stay/free things to do?

I'll be in DC next week for a few days and am flying in. I'm looking for somewhere to stay that is near monuments/attractions/places to go out. I'd rather spend my money on a nice hotel and walk around rather than spend it on cabs! Would be convenient if I could walk back to the hotel after going out! Also don't have that large of a budget so I was wondering what I could do that would be relatively inexpensive? Thanks :)

http://washington.org/visiting/browse-dc/attractions/100-free-things-to-do

for a place to stay, try priceline and pick a 3 or 4* near the mall.