WY climbing & camping recommendations

Planning a trip to Yellowstone (from midwest) later this month (July) and have 3-4 days dedicated to climbing. Thinking about Devil's Tower and Tetons. May split it up, may just go to Devil's Tower.

Looking for lower grade multi-pitches, so have our eyes on Durrance on Devil's Tower and Exum Ridge in the Tetons. Any recommendations for less busy routes? We climb Red River Gorge in 90+ degree, humid heat, so what do we have to consider climbing WY in July?

Due to a tight schedule, we'd like to camp close to the climbing at both Devil's Tower and in the Tetons. Suggestions here, too? Backcountry camping is welcomed with us. Cheap/free is even more welcome.

Other things that I'm probably missing?

Sweetwater Rocks by Jeffrey City has some nice slab multi pitch routes, and Fremont Canyon is always worth a stop.

Not sure if this is still a thing but Frank let's climbers stay at his lodge for free/donations. It's the closest camping you will find. It's called the devils tower lodge and it's within the park.