Of the same kinds, class, or nature

Tomorrow morning I am meeting thekatebeyond in DC. I'm picking her up at National, and then we are going sightseeing.

I *hate* driving in cities. The plan right now is to park the car in one place in the morning, and then not touch it until that evening.

Here's the help I need - where can I park my car? I don't want to drive around looking for a spot, and I know spots in town are very limited.

We're totally good with taking the metro, and plan on spending most of the day on the Mall and in the Air and Space Museum.

So any suggestions for lots in those areas? Or lots near a metro that won't be full by mid-morning on a weekday?