The Washington area is a gold mine of sources for research. Below are the most important sites:
Depository of census records, military records, immigration records, and other records of the national government. To research military records you will need to be there during the day time, M-F, 9-5. Census and microform research is available during all open hours. Archives/Navy Memorial Metro Station.
The nation's largest collection of family histories and local history books. You will want to use the Local History and Genealogy room. I recommend accessing the catalog from home so you know what you want to look at. Expect to kill an hour or two before your first books arrive for your research. These system is clumsy but voluminous. Here, you need to go during the day, M-F, 9-5, if you need to use microform. LOC is microfilming more and more of their old family histories and will require you to look at them in that form if they have done so. Union Station or Capitol South Metro Station.
The second largest library in the city. Open stacks are much easier to use than LOC, but the collection is not as extensive. There is a minimal charge ($5 per day on my last visit), but well worth it. Among the items only available at the DAR are the collections of genealogy materials from the women of the DAR from coast to coast. They even have their card catalog on line now. The DAR library is some distance from a metro line (about six blocks). It is the one location you may want to drive to in downtown Washington, but be prepared to hunt for a parking place and to feed meters. There are no parking garages closer than metros. Farragut Square West or Federal Triangle Metro Stations.
Many of the county libraries in Northern Virginia have excellent collections of published material on Virginia genealogy. Among the best are the Lloyd House Collection (now relocated from Lloyd House to the Barrett Library) and the Virginia Room at the Fairfax Public Library. Neither are close to metro stations and probably require drives. There is a parking lot at the Fairfax Library, but Alexandria is street parking.
For those of us who research in Colonial and early Federal history, there is an excellent exhibit at the National Museum of American History called "After the Revolution." I recommend it highly for those interested in family history as well as genealogy. Federal Triangle Metro Station.