Zion and Bryce don't require guides like Monument Valley does (Monument Valley is in the Navajo Nation/Reservation). Nor do the size or complexity really demand it. Both are small "drive through" parks with some short hikes. The drives are quite popular, the hikes less so but still can be crowded.
In Zion the premier location is Angel's Landing, but the climb is fairly strenuous and you WILL need both hands in several places so have a good bag or backpack for your camera gear. Many don't make it past "the neck" just past Scout's Landing on the way up to the top. There's no shame if you don't: the drop is 1200' straight down on one side and 900' on the other IIRC, and the rock you have to climb over in the middle of the neck is about 3' wide, 3' tall, and sandy (the whole area is sandstone). The Emerald Pools hike is a short, pleasant warmup and pretty. Other than Angels Landing the locations in Zion are all down in the canyon - the roads are at the bottom, which makes it a bit unusual, so "sunrise" is much later and "sunset" much earlier than if you were on the rim.
Both Zion and Bryce are very heavily travelled parks because of their proximity to a major interstate highway (I-15). If it were me with one weekend from Salt Lake City, I'd go either further south to the north rim of the Grand Canyon and drive out to the two very scenic overlooks just east of the lodge (Point Imperial and ?), or go to Yellowstone via Jackson Wyoming and the road past the Tetons.
I was in Yellowstone in July, and the northeast corner of the figure eight road is closed. Mammoth Hot Springs on the far northwest corner is no longer worth visiting, in my opinion: totally dry now. Old Faithful is cliche, but that area is still beautiful and the short hike down through that area is worth it. Lower Falls is on the northeast side, but not in the construction zone. The short but steep hike down yields better photos. Hayden Valley nearby is fantastic for bison with a long telephoto, but I believe inaccessible due to construction. That leaves Fishing Bridge and Grant's Crossing? on the south loop, which are nice, too, but not premier locations. If you go to Yellowstone, stay in Jackson overnight one night so you can get sunrise photos of the Tetons early the next morning. But Jackson is expensive... try not to get sucked in to the shops.
My first choice is still definitely the North Rim of the Grand Canyon, though. That's one place every landscape photographer should go at least once in their life. It really is that impressive.