Hains Point Park in DC has a pool, and is a great place to get some laps in on the bike afterwards.
The Washington Lee High School Pool in Arlington is right off the Custis Trail with connectivity to the W&OD or Mt. Vernon trail.
And if you get in a short run afterwards, that would make for some nice little triathlon training!
Eastern Market in DC has a public indoor pool – on a weekend you can also hit the market for all kinds of lunch options. Nice easy ride from Arlington also that takes you down the National Mall.