If I were you, I would try to do the vacation in late September or early October. Things cool down in southern Utah and allow for a more pleasurable experience.
There are so many cool things to do and see that you will need to pick and choose what is right for you. With that being said here are some of my recommendations if you were to start in St. George and then work northeast.
My favorite place to hike in St. George is at Snow Canyon State Park. Also the Anasazi Ridge petroglyphs are kind of cool. They are north west of town.
Moving north from St. George would take you through Zion National Park. There are many great trails in the park from little trails to a whole Zion Traverse. Zion is cool, but not my favorite.
If you go through Zion you can then continue up toward Bryce Canyon (easily my favorite). There are many great hikes in Bryce. All of them essentially start on top and drop in. Fairyland Loop is a great trail and a little less crowded. Queens Garden and Navajo are pretty popular, but for good reason. Star gazing is also a specialty of the park as well due to its remote location and no light pollution. This park is at elevation and therefore can get chilly.
From Bryce you can head over toward Escalante and Grand Staircase National Monument. A popular hike here is Calf Creek Falls. It is well worth the hike. The waterfall is pretty spectacular, and if it is hot you can swim at the base of the falls. We have done it early in the morning and had the place all to ourselves, and then passed all the hikers on our way out.
Continuing north from here you can head up to Torrey and Capitol Reef. Again there are plenty of places to hike.
Heading west from here will take you over to Hanksville and then going north Goblin Valley State Park is worthwhile. Right by Goblin Valley is Little Wild Horse & Bell Canyon is a great slot canyon hike to do as well.
From here you can head over to Moab area and hit Arches National Park as well as Canyonlands. The most popular hike at Arches is probably Delicate Arch, but there are many more hikes to do here. As far as Canyonlands, you could spend days here. It is a very large park with 3 different entrances to the park area. While you are in the area, Dead Horse Point state park is unique and has a very famous photography point high above the Colorado River.
If you do that, then congrats you have visited the
Mighty 5.