I'm from Utah, and I love it there. most roads through southern Utah will take you to view some pretty great scenery.
While Arches and Bryce are both crowded ( as well as Zion NP) of course you need to see them. Canyonlands is so big, you could spend weeks there and it is not very crowded. Moab is a pretty fun town and the area has lots to do outside the national parks. other hikes, rock climbing, canyoneering, mountain biking trails, rafting, breweries. Dead horse Point state park is around there with a fantastic overlook of the river and canyonlands.
I don't know which way you are driving to get between them, but Capitol Reef NP is really nice and rarely visited, Red Canyon in Dixie national Forest ( near Bryce) is beautiful, has some great hikes, and Butch Cassidy had hideouts there.
Cedar City has a wonderful Shakespeare festival close to this time of year IF there is anything going on when you'll be there I'd highly recommend a stop- It's really, really high quality ( they do other plays as well as Shakespeare). Brian Head Ski resort is a great place for lift access mountain biking in the summer or hiking, the elevation is up there- so if it's too hot down below it's a great place to spend a cooler day- often need a long sleeve shirt even in July. ( eagle point ski resort is down in south central utah as well, it used to be elk meadows when i lived there, probably has some similar activities- this is in the Tushar mountain range which is very beautiful, and not that traveled)
Big Rock Candy mountain resort is right on the 89 after you turn off I 70 on your way down to bryce, they have a lot of activites there, and if if you don't stay, it's worth a stop to see their unique brightly colored mountain ( and the lemonade springs :) )
Kanab is a quirky town that is fun to visit, great vegetarian/vegan eateries too, about half the people that live there work up the canyon at the Best Friends Animal Sanctuary- where you can take a tour- they do great work there for animals of all kinds. near Kanab is the pink coral sand dunes state park.
And if you decide to make a visit to St George area- snow canyon state park is one of my favorites with some fun hiking on sandstone (much less crowed than the NP and little more leeway for off trail goofing around). And if in St George, you must go to Swig's and get a sugar cookie- the best ever! ( and I'm not usually a fan of sugar cookies, but this one is perfection)
what every you end up doing, enjoy your trip!, I haven't been in southern UT for over a year, currently exploring the pacific NW, but Utah will always be home!