My Utah Handbook by Moon Publications shows a large number of campgrounds along the Mirror Lake Highway, UT 150. My memory recalls it as pretty scenic, and nice to visit. The road is fine, not too many services though, at least back in 1979. It says it gets crowded, though it is now off season. Don't know about mosquitoes, and I guess there are bears and mtn lions. Maybe check with the USFS, they seemed to know a lot.

There are many NFS campgrounds between Kamas and Evanston (12-15?) but the most scenic, imo, are the ones near Mirror Lake (Moosehorn and Mirror Lake CGs) but they do close sometime soon.

There are also some areas for car camping that are not at a fee campground but these are not as plentiful as one would think. They are there off the main road but many lie on the several dirt (and rough) roads of off Mirror Lake Highway. There is a flat-ish section to the left of the road just before the last push to Bald Mountain Pass (coming from Kamas). There are campsites here although most are not "super" private.

There should be no bugs this time of year... or very few. I have spent many nights in the Uintas and have never seen a bear but they are there.