Check the Beacon Hotel on 16th and Rhode Island NW. They take reservations for tables in their rooftop lounge on the 4th even if you're not staying there. It's a little ways from the Mall but great view from the roof, and a fraction of the crowds.

And most restaurants will indeed be open, except those that cater exclusively to an office worker type crowd.

Getting a taxi from Union Station to Foggy Bottom will be no problem. Taxi from BWI will be very expensive though. Car service to/from the airport pops up on Groupon about twice a month.