You can take a trolly that will guide you around D.C. and will allow you to get on and off at certain stops thats pretty cool. (
http://www.dctours.us/tours/tourDetail.cfm?tour_id=8827&gclid=CIrgsMaf3JICFQQIFQodkVt8_A)
However, I think that the best way to enjoy D.C. is to get onto the metro and just jump on and off certain locations. (
http://www.wmata.com/metrorail/systemmap.cfm). McPherson on the orange line will bring you to the white house, 3 stops up on the orange line will bring you to the smithsonian, where all the main museums are and the monument. (and I think all of the museums here are free). If you get off at Foggy Bottom, take a cab and ask to go to M street. That's Georgetown, where all the really nice resturants and shops are. Chinatown on the Red Line isn't bad either, it has a TON of shops and places to eat!
You can also go to the zoo if you'd like! (
http://nationalzoo.si.edu/Visit/GettingToZoo/) You can get to it on the Metro Red Line. Take the Red Line to the Woodley Park/Zoo/Adams Morgan stop or the Cleveland Park stop. The Zoo entrance lies halfway between these stops, and both are a short walk from the Zoo. The website also has other ways of getting there too.
If you're renting a car and want to, you can drive to Baltimore. From where I live in Norhtern Virginia, it's about an hour away, so, I know from D.C. to baltimore, it's not that far, but, I don't know the exact time distance, sorry! But, they have a ton of great shops, great seafood and the aquarium there too. (
http://www.aqua.org/?gclid=COjSi96h3JICFQdbHgod0WLniQ) I haven't been there since I was little, but, I remember it being fun and huge!!
This site will help a lot for planning your trip too:
http://www.si.edu/
Honestly tho, you can prolly see all the monuments that you want to in a day, museums on another day and shop on another. I've lived here for 14 years and I find D.C. pretty boring considering it's our nations capitol. But, I have the most fun walking around D.C. especially georgetown at night! it's so lively and, there are a ton of clubs and bars to check out.
Hope this helps!