I rarely have any problems shooting shooting around the Mall and I've usually got my tripod. As long as you're not blocking people, you should be ok. It's hard to find people around the Mall and museums without cameras. The security staff at Federal buildings are generally uninformed, confused, and unacquainted with the law, so you may be hassled in order to fill their empty incident logs. Staying downtown is very expensive, so you might want to look for hotels near metro stops--which will be merely expensive. I think the Hampton Inn on 6th and Mass is good and further out--the Embassy Suites in Chevy Chase, would be worth checking.