Sounds like you are in Colorado with a car and some time to kill. No? Why limit yourself to the immediate area? A whole lotta people would kill to be in your shoes.
If it was me, I'd drive 2ish hours west to Buena Vista and camp somewhere in the Collegiate Peaks. It is B-youtiful around there, and the drive is pretty scenic too.
From *THE* traffic light in BV head west up towards Cottonwood Pass and camp off the side of the paved road or in one of several USFS pay campsites.
Or with a tiny bit of driving on a dirt road, the Cottonwood Creek trailhead (for the Colorado Trail) just NW of BV is beautiful. Pit toilets and about 50 yards to lug gear from your car to quiet creekside free camping.
I don't recall exactly, but I'm pretty sure all these options are well above 10k feet. And there are 2 (pay) hot springs in the area. For daytime amusement, you can head 30ish scenic miles upstream to Leadville and rub elbows with folks preparing for the LT100 on Saturday. LV is a fun, funky town to pass some time.