Do you HAVE to stay in the District itself? You can usually get better deals staying in Maryland or Virginia at hotels near the subway stations and taking the trains to where you need to go in DC. My favorite neighborhood is Crystal City in Virginia. There are several hotels within an easy walk of the Crystal City metro station (and one hotel is at the station). The Yellow Line quickly gets you to DC. Of course, as others have also asked, where exactly in DC do you need to be?

If you do indeed want to be in DC itself, given that you will be arriving at Union Station, which is on the Red Line, have you considered the Hampton Inn Washington-Downtown-Convention Center? It is a short walk from the Gallery Place Station, which is just 3 minutes by Metro from the Union Station Metro station. I stayed there once and enjoyed it. There are a lot of food options around Gallery Place, including authentic Chinese.