Hi. I'm very familiar with the area. Actually my father lives there.
I don't know of any free boondocking in the immediate vicinity (other people, if you do please speak up). There are however, lots of state parks around as well as national forest with developed campgrounds.
Outdoor areas to see:
- Vedauwoo (pronouced "Vee dah voo"): An awesome formation of boulders, about 28 miles west on Happy Jack Road, or the other end of the formation on I-25. It has a developed campground that's a per night charge, but I don't think it's very expensive. It also has a large (a couple of square miles) day use area where you can go hiking on the rocks and "climbing at your own risk". It is somewhat similar to Garden of the Gods in Colorado, but I personally like Vedauwoo better because it's not covered with sidewalks.
- Other national forest: Past Vedauwoo on the right side of Happy Jack Road there are other national forest areas. There's an old concrete bunker up there, lots of trees, and some campsites. It used to be free boondocking, but it might be paid now.
- Crystal Lake, Granite Lake: These are the low reservoirs for Cheyenne, about 15 ish miles west of town. Fishing and boating mostly. And in August, people watching, because they'll be crowded. The camping is state park I believe; make reservations on their website. (Reservations are currently required for all state parks because of the health situation.)
- Hawk Springs: About 70 miles northeast. An area surrounding a river and small lakes with trees and campsites. Camping is state park.
- Guernsey state park: About 80 miles away, north on I-25 then east on highway 26. Another lake area. Lots of state park campsites. This is right next to Guernsey Army Base, which is primarily a National Guard training center.
- Glendo Lake: About 80ish miles north on I-25. Largish lake, very deep, maybe 80 to 100 feet. Fishing, boating, camping. Completely surrounded by campsites. I think the camping is state park. Warning about August though: They drain Glendo every fall and give the water to Nebraska, so if you get there too late it will be a low swamp rather than a lake.
Museums: Wyoming State Museum, Old West Museum. Wyoming Archives (old documents). These three are in Cheyenne proper. The state museum and archives are downtown near the capitol building, and the old west museum is right near Frontier Park.
That's all I can think of at the moment, but if I think of more I'll post again. Also, if you have any specific questions about the town I probably know the answer.
Cheers.