You can camp at the Lewis Lake campground. There is a good trail from there to Shoshone Lake which is a beautiful large mountain lake.
As mentioned be sure to get the back country permit first. The rangers will brief you on what to do and watch for.
Also keep a good distance from all wild animals. Especially bears, Bison,Moose, and mosquitoes. Sorry impossible to maintain distance from mosquitoes which will be a problem with any back country excursions. Even an innocent looking Doe that has a fawn close can be a problem.