My husband and I have stayed in DC several times for $100/night by booking at the smaller boutique hotels. They are nice and often have a decent breakfast or happy hour special or freebies. Best of all, they are super centrally located and usually in neighborhoods. I signed up for their free clubs and that's how we got our rates. Not sure if you want something under $100, but I do know that these smaller hotels give you a nice feeling of being in the action and are, to me, a little more interesting and somewhat more special as a trip. We are usually only in DC a night or two, though, so we generally see it as a quick vacation!
I've also stayed in the National Harbor area and it's beautiful. If you have a longer stay, I know the timeshare there (Wyndham) is amazing and you may be able to rent points to use it! My inlaws own and we've stayed there several times, too.