Andrew14302, The Grand Westin in D.C. is my second home. :-)

Self parking is $15, due when you pull in. (If you don't have cash, though, you can pay when you leave in the morning). The garage is shared by the office building next to the Westin...it's not owned by Westin.

Valet parking is $24. Cars are parked in the same garage as self parking. Valet parking is billed to your room.

I prefer to self park rather than wait to have my car delivered. The few times I have used valet parking, though, my car was retrieved very quickly.