Almost any school in the western US is within comfortable reach of good back country. Those in major urban areas (LA, Denver, San Fran) are a bit more inaccessible. Think northern locations if you want winter sports.

My favorite, and I am prejudiced because I am a graduate, is the University of Arizona, just a bike ride away from trail heads, with lots available just a bit further away. Gets a bit warm in the summer, but higher, cooler country is easily accessible.

Frankly, this should be a secondary factor in choosing your graduate school, well behind the presence of a competent, accessible faculty. Develop a list of good schools and see which ones are close to the outdoors. Grad school isn't forever.

I was lucky - the UofA was listed regularly in the top five in my field when I attended (way back in the Pleistocene).