The GH is basically sitting on top of a subway station (indoor connection) which is a great advantage in DC. You don't want a rental car and the metro is a new system that's generally pleasant and easy to use. Tyson's Corner is a suburb which doesn't feel like part of DC. If you want to be outside of the district but still in an interesting area, check out whether there are any Hyatts in the historic/downtown area of Alexandria.

Breakfast at the PH is extremely good.