There is a very good high speed rail connection between NY and Washington. The Stations on both NY and DC are real icons. I think you would have a hard time just seeing the Air & Space Museum, Natural History Museum and the National Art Gallery in two days. The greatest gold coin collection in the world. There are a lot of great places to eat and shop too - most reachable by the great DC metro system. I lived in Alexandria, VA for three years and never ran out of places to visit or things to do. In any case, enjoy your visit!!