We stayed at the Radio City Apatments (in a one bedroom suite) in November last year. I have done a bit of a review about it one of my other posts. In that, I was adament that due to a problem with the water pressure, I would never stay there again. Well having had the time to think about it some more - I have changed my mind. Would definately give it another go. It simply has too much going for it. Price, space & the phenominal location. If I had a problem with the water pressure next time, I would be more assertive in getting it looked at & if it could not be fixed, then being shifted to a different room. By the way this was the second time we had stayed there & the first time we didn't have an issue with the water.
In Washington DC we stayed at the State Plaza Hotel, which had some really affordable options for larger groups. It was also about an (tops) 8 minute walk to the White House & a 15 minute walk to the Lincoln Memorial. Just be aware though, that this hotel has two big buildings & the one further away from the reception area seems to get bad reviews, while the closer one gets good reviews. We stayed in the closer one (actually the suite right above the reception area) & although it was an older type accomadation, the space was massive. Also as a general rule, hotels in DC are a lot dearer during the week, than on the weekends. (Opposite rule in Las Vegas).
Hope this helps. Oh & my number one helper for choosing hotels is the reviews & photos on tripadvisor.com!