Gallaudet University - It is a college for the deaf.

If you'll be there in 3 weeks it'll still be pretty cold/rainy/snowy...something indoors might be better just in case C&O/Potomac River is out of the question. I always enjoyed going to Union Station on lousy days - they did a beautiful job restoring the inside and there are shops to walk around.
Take metro down to Old Town Alexandria and walk around artists studios at Torpedo Factory. Mt Vernon is a good suggestion. The zoo might be fun if it isn't too yucky outside - it's free anyway.

Do you plan on visiting Mount Vernon during your 3 day weekend? If that wasn't in your pans, then that's my suggestion.

Have fun!

There are quite a few wineries in the Virginia countryside. They are usually quite nice, have snacks and you can try some wines of Virginia.

Also, you might want to check out some of the battle sites from the Civil War in Manassas, Virginia.

Also, every parent is different, but when our child was under 1, we used to go to lots of happy hours (smoke free) and she just slept happily while we sipped our cocktails! There are lots of nice places to have a drink, or even Tea. Tea might be a good choice at the Four Seasons, the Ritz Carlton or the Mayflower hotels. Beautiful and elegant hotels and a warm way to spend the afternoon.

One more thing: Be sure to take a 'drive around' tour of the monuments, Capital and White House at NIGHT. Entirely different from daytime and spectacular!