There is a RI on Vermont Avenue NW that is very close to the Smithsonians, the Mall, etc. that may meet your needs.
I have never personally stayed there, as I live in DC, but have had visitors stay there. They have always been pleased, and you can't beat the ability to get around town from there.

I guess it depends on what you want to visit the area for. If you want to be near the historic stuff, try the RI or the courtyard at 9th and F St (near the Spy Museum. . cool stuff). If you are bringing kid(s) and want to be near the zoo and a little more residential area, try the Wardman Park Marriott in the Woodley Park neighborhood (close to the zoo, a Metro stop just down the street, lots of restaurants). I used to live just down the street and really am a big fan of the neighborhood. Plus, if you have a car, you'll be right on Connecticut Avenue, and you can get almost anywhere easily from there. But I do recommend the Metro for sheer ease. Enjoy your trip!