As mentioned above, most of the museums and monuments are on the National Mall, so this is probably where you’re going to spend most of your days. Be aware that the National Mall is extremely large, and it’s a punishingly long walk from one end to the other, so bring a map and plan accordingly. Also, the “Smithsonian” metro stop is not the best stop for all the Smithsonian museums.
Museum hours vary and some museums are open late. Some attractions (such as the Holocaust Museum and the Washington Monument) require timed tickets. Check hours at their websites:
si.edu/Visit/Hours
nga.gov/ginfo/index.shtm#hours
Restaurants and shopping on the Mall are extremely limited. Your best choice for lunch is in the museum restaurants (the American Indian museum cafeteria has especially good international and healthy options.) To find a restaurant for dinner, walk from the Mall toward the Archives, Gallery Place, Metro Center, or Foggy Bottom metro station (whichever is closest to where you are).
The metro is undergoing some extensive maintenance work, and some stations are closed on weekends. Check out the schedule before your trip:
wmata.com/rail/trackwork.cfm
Regarding hotels, don’t rule out staying in a downtown hotel before you check the discount rates. I’ve found some very good hotel discounts on Expedia and Hotwire. If you decide to stay in the suburbs, carefully check the location of the hotel on a map relative to a Metro station. If the Metro station isn’t within walking distance, look for another hotel. You’ll waste too much time waiting for the hotel shuttle, or if you try to drive to the station, you’ll be frustrated when the station parking lot is full. There is no free weekday street parking anywhere near any metro station or anywhere in downtown DC. Also, for safety reasons, avoid the hotels near the New York Avenue metro station (and the neighborhoods around the Silver Spring station can be iffy at night.)
If you decide to drive into the city rather than take the metro into the city, then your strategy will change a bit. Find a hotel with free parking (and double-check that the parking is actually free). You’re probably better off staying near the beltway in Maryland rather than staying in Virginia, so you can take surface streets all the way downtown and not worry about the HOV lanes and congested bridges. Don’t bother looking for on-street parking – you won’t find it unless you know where to look; instead, reserve a prepaid garage space at
bestparking.com
Many of the other posters’s suggestions are far away from the tourist areas, so double-check the map first, and remember that it will take longer to get anywhere than you think.