Yeah, I was going to recommend tours too. One that you can get on and off as needed at Mall etc. locations is good (e.g., Old Towne Trolley). You might be able to get miles by booking it at
www.viator.com
Look at the Metro maps and station information on
http://www.wmata.com/
Click the links to Stationmasters for maps of what's around each station.
(Smithsonian station is in the Mall. Federal Triangle is just north of the Mall. Metro Center is the next station north of that. Capital South or Union Station are Capitol Hill (kind of pointless, though, unless you have a weekday res from your Congressperson for a staff led tour).
Check Smithsonian.org for special exhibits. Also, I think the museum of American history is closed for renovation.
There is much more (e.g., holocaust museum, not a happy experience, but a must-do in this lifetime).
And my all time favorite place in DC:
http://www.phillipscollection.org/.
Dupont Circle Metro stop, use mapquest or equivalent to locate the address from Dupont Circle.
PS: hope you are getting the $69 special for September weekend nights that hotel offers. Otherwise why stay way out there.