Thanks for all the suggestions.

For now I've booked the GH Denver. It'll be a bit more of a hassle to get to late at night, but worth it for the chance to experience a bit of the city, and it looks like it might have the best pool/exercise facilities, which would be nice before a long flight.

For getting there and back to the airport with a family, would you recommend a rental, the train or an uber/taxi?