Ok well first thing you have to realize is the smithsonian is NOT one building

Its really like 10 buildings...
If you'd like if you wanted a hotel in VA sometimes the hotel will have a shuttle service to the metro station. The metro can take you to the smithsonian stop in DC which brings you within eyesight of a number of museums

The metro will also take you within a block of spy museum if you wish
Ohhhh also suggest cheesecake factory for food

Yea I liked spy museum, it was pretty cool
Its a linear walkthrough museum, you follow the passageways. There are lots of movies to watch and lots of gadgets
Also from the spy museum stop (can't remember which one, theo may know.. I know its on the spy museum website) you can walk a couple blocks and get to the whitehouse if I remember right...
Depending on when you're going some places you'll have to get to REALLLLLLLLLLY early in the morning (around 7/8ish) to be able to get in. (white house, and washington monument are really bad for this) spy museum at least this past summer we got there at 11am and the line was wrapped around the opposite side of the block

.. so we went early and it was only around one corner of the block
MarriottA friend of mine really likes this marriott in falls church. They have a shuttle that takes you to the metro station, and has a pool and whirlpool and overall a nice hotel. If you stay over the weekend you maybe able to get their 60 or 70 dollar a night rates instead of the weekday rates (120 a night I think). Its not hard to find, but not much around it.. unless you drive like 5 miles away is tysons corner where there is quite a bit of stuff

I don't know any hotels IN DC .. Theo maybe able to help with that
http://www.wmata.com/default.cfm this site is a huge help

You put in your destination and your source, and it'll tell you which trains to take and which buses if necessary

Most times if you ride into DC on the metro the places should be within a good walking distance.. given you're going on a below freezing day