I recently took a two week road trip staying mostly at Hyatt hotels to hike around new trails. I personally stayed at (and hiked around) Hyatt Place Moab (close to Arches National Park) and Hyatt House Provo Pleasant Grove, which is close to trails around Provo Peak, Spanish Fork and Loafer Mountain.

In my home state of Washington both the Hyatt House Bellevue and the Hyatt Regency Lake Washington are good options to explore the trails around I-90. Suncadia is next to Roslyn and there are tons of hiking options in the area.

I plan to visit Sedona in the fall as I've also heard there are great hiking options around the area.