Well not everything west of T-dad...
I went to that school 30 years ago. You will have a good time! At least the town is in slightly better shape now than it was then (ahem).
Well west (about 30-40 minutes) of T-dad on Highway 12 there is Bosque Del Oso state wildlife area on the south side of the highway, and Spanish Peaks state wildlife area (two tracts) to the north side. There is a patch of BLM to the northwest, but it is surrounded by private land and access may be iffy.
Further west on 12 there is a chunk of San Isabel National Forest up in the Culebra/Spanish Peaks mountain range. That area is so beautiful (Hwy. 12 from Stonewall north to Cuchara Pass) that it will break your heart, especially in September when the aspen leaves turn gold. But much of the Culebra range is private.
Far to the east and also northeast there is the Comanche National Grassland public lands, but it's VERY far. For yotes your best bet is getting permission from local ranchers.
Further north and west you have the Wet mountains and Sangre De Cristo mountains, public national forest. The Sangres are big, big, high rock sawteeth, like the Alps. The Wets are more gentle and rolling, thickly wooded.
Beyond this there is way, way, more, but it's a heck of a far drive.
Get yourself a state map from the Dept. of Interior Bureau of Land Management that shows the land ownership by colors, it will show you all at once where all the public land is. That and the large red Delorme State Atlas and Gazetteer will let you navigate anywhere.
There is not much to do in T-dad, except drink, so be forewarned. Bring lots to read. The school library has a great gun book room, and there is a small but really good geology museum below the library around back. In my day we could keep our guns and reloading equipment in our dorm rooms, but no longer - rules are a lot stricter. On the other hand, the NRA Whittington center range complex is about 35-40 minutes south over the state line, so you can indulge yourself there.
This state is huge and has wildly varying terrain, so be prepared to do some exploration before you really understand what this means. The elevation controls the type of plants and ground cover, so from high to (relatively speaking) low, there will be huge changes. It is not all similar, as the midwest or east tends to be.
T-dad was my first taste of Colorado and the west (I'm a Jersey boy originally) and it really put the hook in me for life. When you get out there drive highway 12 out to Cuchara Pass (between the Spanish Peaks and the Culebras) and you may never be the same again either.