One of my favorite spots near Pinedale is just a bit south on your way to rock springs. It is a campground named Weeping Rock or another is Slate Creek. They both sit right on the green river. This area is just below Fontanelle Reservoir. That time of year will be on the warm to hot side but the fishing can be out of sight. Plan on the wind picking up in the afternoon and shuts off around dinner time. There are some BIG BROWNS to be had especially on a fly. I prefer to strip large articulate streamers. There is water available at Weeping Rock (I think).
In northern Utah another member mentioned Browns Park or Indiana Crossing. This sit well below the Flaming George Dam. The fishing down there I think is pretty good. I don't believe it get much pressure only because it is a take out for the "B-section" and most folks are heading back to the lodge or their camp up near the Dam. This spot is a bit of a commitment because it is about 20 or 30 miles down a half dirt and paved road. It used to be the last five or so miles was a nasty steep dirt road, however a few years ago they cut out the side of the mountain and laid an brand-new two lane paved road with a mellow grade and guardrail. Its so weird because it almost seems like the quality of the road is so out of place for the rest of the road in. Anyway there is water available in Browns Park near Jarvis and the sits are nice. There is not a lot of info to be found on either B P or Indian Crossing. I prefer I C because its a bit closer to the Green and I can take the kids down on a quick float to cool down in the middle of the day with out making the wife nervous regarding rough water. To get to I C you do cross over the G R just before you get to B P.
There Red Canyon area is nice as well , lots of great views and much cooler that time of the year. It also is next to the best eats in the area for sure.
Feel free to message me if you have more questions.
Have a great trip