On the east coast, Alexandria, VA is a place you might not have thought about. The ALX Amtrak station is right next to the Metro King Street Station. By Yellow or Blue lines on Metro, Reagan National Airport is less than 10 minutes away; cost is $1.85 to $2.25 depending on time of day.
Motels are quite close to the King Street/Old Town Metro-the nearest I can think of is an Embassy Suites across the street from the Metro exit, but there's a Hilton and a Hampton Inn less than a quarter mile away and plenty of others within a half-mile. Old Town Alexandria is well known and popular for its shopping and food amenities.
Obviously, Washington D.C is another potential Amtrak location near the Reagan National Airport. Metro Red Line serves Amtrak WAS Union Station; to get between WAS and Reagan National, you'd transfer between the Red and either a Yellow or Blue train. The shorter trip is via the Yellow line, with a transfer at Chinatown-Gallery Place; using the Blue line, the transfer point is Metro Center. Cost is about $2.05 to 2.70.
Landing or taking off from Reagan National can be a thrill! On a clear day with a good seat and takeoffs/landings in the right direction, you get to see nation icons like the Washington Monument, Arlington Cemetery, the Capitol building and Mall as you fly above the Potomac River.