What part are you thinking of visiting?? There is a lot of Hells Canyon accessible from Cambridge, ID, which includes Brownlee and Oxbow Reservoirs. This section is also accessible from the Oregon side. There is good camping at developed campgrounds as well as plenty of boondocking opportunities.
Then there is the section accessible from White Bird ID, which is where I live. I actually live on the road that goes over to Pittsburg Landing in Hells Canyon. There is a wonderful developed campground right next to the river. The Snake River in this section is free flowing and a designated Wild and Scenic River. It’s spectacular down there, right in the heart of the National Recreation Area. As others have mentioned, it might be hot in June. But it will cool down at night.
Of the two, the section from Cambridge is much easier to get to. But there will be tons of people there, many fishing Brownlee Reservoir. There will be way fewer people at Pittsburg. The road over is a well maintained dirt road, but it’s pretty steep on both sides. I have to put my tow vehicle in 4WD towing my 19 home, even when the road is dry (back tires spin on loose gravel), but it’s no problem.
If you wanted to visit this section of Hells but are unsure about towing on this road, there is a wonderful BLM campground just outside of White Bird called Hammer Creek. It's a wonderful, quiet campground with lovely sites right along the Salmon River, with no worries about towing on a steep, dirt road. I’ve never seen it crowded. You could set your camp up there, then drive over to Pittsburg for the day.
Many options! If you have any questions, don’t hesitate to ask me