I strongly recommend staying at the Willard. It is a very beautiful historic hotel (Abraham Lincoln and Martin Luther King Jr. stayed here) and well-located hotel. You are literally 2 blocks from The White House and a 7 minute walk to The National Mall where most of the National Monuments and Smithsonian museums are located.

You definitely don't want to drive in DC. However, we rented a car since the cost of the rental + gas + parking a block from the hotel was ~$100 or much less than the cost of a cab to and from IAD.

I've posted a detailed trip report on The Willard with 34 pictures on my blog from my trip 2 weeks ago.

Have a look at the pictures and perhaps you'll want to stay at the Willard