Which places are the best in washington for sightseeing?

This is a pretty good list.

http://www.planetware.com/tourist-attractions/washington-uswa.htm

I always recommend that people see Arlington National Cemetery when they're in DC.  It's a very historic and honorable place to visit.  Very impressive and sad how many people of all walks of life are buried there.

If you are in Washington DC start at the Lincoln Memorial and work your way up the National Mall. You will be in walking distance of the major monuments and museums.  Right now and for the next year or so they are upgrading the "subway" system so expect major crowding and delays. Walk when possible.