I'm planning to take a trip to Washington DC for a long weekend and would love it if I could just fly/train there, use public transportation to get to a hotel & get by without a car. Is this possible? What's a good place to stay (going to Smithsonian)?

By all means, don't rent a car. If you're flying into National/Reagan airport, the metro subway goes right to the airport, and you can take it to just about any location. A car is a hassle to worry about, and you definitely don't need it in DC.

I would echo jon's comments re: transportation. Just stay at someplace near the Metro.
If you want historic but $$$, the Willard or Hay Adams are unforgettable.
The botique Monaco is unique.
If you're looking for something more moderate, a chain hotel in Arlington/Crystal City/ Alexandria should suit you fine.

Forget the car. I was in Alexandria for a convention by myself and took the Metro into the city to see everything. The Metro was very clean and safe and easy, and hit all the top tourists spots except Georgetown, which I cabbed it to.

Forget the car. I live here and rarely use the car to get around the city.

Several years ago we were in DC for 3 days. We had a car (road trip) and never took it out of the hotel garage while we were there.

On my first visit to DC, like J_Correa, I also rented a car ... and paid as much to park it 3 days as the rental cost! Since then, NO way I'd have a car. Reagan/National *IS* the most convenient airport, but public transit works well from BWI and Dulles/IAD too. I prefer BWI for a compromise on flight cost and ground-transit cost/convenience over IAD. And of course there are cabs & shuttles. As long as you don't stay too far out of town, as long as you're near a Metro, you're OK for getting to any DC Smithsonian (and there are several!).

Ditto -- you will definitely not need a car. We were there in April and stayed at a hotel in Old Town Alexandria only a couple blocks (if that) away from the Metro. Took it in to DC to visit all the sites. So convenient! Just make sure to fly into Reagan Airport.

Enjoy your trip!