If you're on the full version of the website there's a sidebar that lists the top questions around DC and the first link is "How do I get from the Airport to DC". It's constantly updated as options change.
No one hotel is truly close to all of the attractions but there are literally hundreds of hotels that are close to some or at least close to a metro station which is pretty extensive and covers a lot of what you'd want to see.
The most convenient area to stay is downtown near Metro Center, which includes Penn Quarter. But if you prefer a more residential area, you have several choices. Lots of topics already here about picking a hotel.
Probably the best areas for easy access are either right around Metro Center to Freedom Plaza OR Penn Qtr. But of course, hotels cost more there. It's easy to get by metro down there anyway from other places, like Dupont Circle. Just stay within an easy walk of a metro stop. Foggy Bottom is also pretty easy, if you are near that metro stop.