We stayed at the Comfort Inn at St. George this summer. It was a good value. Zion is like Disneyland (crowded) so be prepared for that. If there is no parking in the lot, park in the furthest shuttle stop from the park. You'll find parking easier and the shuttle will be empty when it picks you up. The closer you park to the park, the less likely there will be a space on the shuttle. Our shuttle passed at least two stops full of people because it was full.
If you want a nice place in St George stay at the Inn on the Cliff or rent a house. Definitely go to Kolob Canyon. I think it’s like mile 39 on the freeway. Beautiful and not so crowded
Haven’t been to Bryce for awhile. You could stay at Ruby’s Inn. Or stay at Brianhead and drive in to the park. Cedar Breaks is not to be missed either
It does get hot in the summer and you can’t drive through Zion they have shuttles
As BigWigRabbit said, June will be crowded. If you are into hiking and don't have a fear of heights, Angels Landing is a great trail with a beautiful view.
When DH and I go to Zion, we stay in Springdale, which is the small town next to Zion. Last New Year's Eve we stayed in a nice hotel with an awesome view and we were the only guests. The park was almost empty too, but the Angels Landing trail was closed due to the icy conditions. There is a nice mom-and-pop Thai restaurant in Springdale.
I haven't been in Bryce in years, so I can't say much about it.
We've stayed at the Hampton Inn and the Cliffrose in Springdale and had good experiences at both. June will be hot and busy, but beautiful. Springdale has a variety of restaurants and some shopping as well. We found some little cabins near Bryce, I can't remember the little town we were in. There are a couple of hotels near the park entrance but you probably need to book really early. I agree that Cedar Breaks is worth a trip. We found it by accident but enjoyed our visit.
Bryce Canyon is one of my favorite NP.
You must go to Cedar Breaks and Kolob too!
If you can go at the end of June, the Cedar City Shakespeare festival is really worth it: https://www.bard.org/plays/2018/
It's not as hot in Bryce as in Zion but both places are so beautiful...
We had wanted to stay at a place called Ruby's, but it was full when I went to make the reservation. I think a lot of the bus tours stay there, but it had a good location. We stayed at a Comfort Inn in Cedar City. It was convenient to both parks, and we went to Cedar Breaks, too. Enjoy your trip. I am very jealous!
I second WacSingLof's post on the Cedar City Shakespeare festival. DH and I just happened to be there last year in summer and learned from the staff at the hotel where we were staying about the festival. We got tickets and saw The Three Musketeers that evening. So much fun. We stayed in Cedar City again this year as it is half way on our road trip between Jackson WY and So Cal, but arrived too late in the evening to watch a play. There isn't much else in Cedar City, and I have not been crazy about their restaurants.