Where to travel solo for November vacation in US, want to enjoy nature

I took a week of vacation time in late November, but I still haven't figured out where I want to go. I'm traveling solo out of DFW and was looking for somewhere I could go to enjoy "touching grass." I would love to see some pretty mountains and forests, maybe do a little hiking. A cabin seems fun, a lodge sounds even better, but my vacation budget is about 3k so I don't know how nice a place I can stay if I still…