Shadow Mountain dispersed camping is just a few miles across the way from the Moose, Wyoming, entrance to Grand Teton National Park. I've stayed here several times at different sites and always had a memorable experience. There are great views and relative seclusion wherever you find a place to camp. Bring your own water and plan to dispose of your waste. All the spots I've been to had cell reception, as well. The road is doable (depending on weather) with smaller cars with careful driving. Higher clearance may be more ideal. The best part is that it is free.