I stay in Denver all of the time. The GH and HR are my favorite Hyatt properties and both are right near the 16th St Mall area that has lots of shops and restaurants. It's 30 minutes to the airport from either hotel. I would take an Uber back and forth which should cost no more than $20 each way. There is nothing to do in the areas around the airport hotels, I'd definitely stay downtown if you have never been to the area.