Depending on how far you want to drive and whether you like the area, we've enjoyed numerous weeks long vacations...in the Great Smoky Mountains.
While nothing like the
"real" mountains of Colorado or Montana, they at least provide some nice views...and usually cooler temp's.
Our preference is in the Cherokee, N.C. area, because it's still pretty close to places like Gatlinburg and Asheville (a little over an hour to each)...but not too close to their daily hordes of tourists.
Here's but one of a plethora of sites that rent mountain cabins...on a nightly/weekly/monthly basis.
Cabins near Cherokee in the Great Smoky Mountains