You'll get lots of ideas for the other parks, so let me pipe up on Great Basin NP. First, pay attention to some of the artwork along the side of the road on your way into the park. Of course there's the caverns and the drive up the Wheeler Peak Drive, but once you're up there, take the hike to the Bristlecone Pine Grove and then beyond to the Rock Glacier. They have labeled some of the trees with plaques telling you how old individual trees are. The rock glacier beyond will make you think you are in the Sierras of California, not the deserts of Nevada.
I'm wondering if the steep climb rbtglove was thinking about was to Wheeler Peak CG, not Upper Lehman. The road to Wheeler Peak has grades up to 8% and vehicles and trailers over 24' aren't allowed. We have mostly seen tent campers up there. The CG's in the park are OK (Upper Lehman is better than Lower Lehman), but we now stay at Cave Lake State Park outside of Ely. Ely is an interesting old mining town to poke around in, and the Northern Nevada Railway still runs weekend trips in October. Check out one of the steam powered trips.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)