When are you planning on traveling?
The closest town of any size to Bryce and Zion is St. George, Utah. But if you are traveling in the summer it would be very, very hot in St. George and not conducive to spending time outdoors. If you fly in and out of Salt Lake City, Park City, Utah is a mountain ski town that would offer many outdoor activities.
Also, not sure if you know that the North Rim Grand Canyon is only open between May 15 and October 15. You would want to stay overnight there at least one night. Two nights would be better. There's one lodge at the North Rim. It books up a year in advance.
You need to move around to enjoy it the most. Springdale is best for Zion so you don't have to deal with parking each day to go in. It has lots of places to eat and easy access to the park. For Bryce you can stay in the park or at Ruby's at the gate. The North Rim is far from any towns. You need to stay in the park and get reservations way ahead or Jacob lake 45 miles away which is not a town but a restaurant/cabins/motel.
For example Springdale is almost 3 hours to the north rim and at least 2 hours to Bryce. Kanab is in the middle but offers poor access to Zion because of the need to be there early for parking to use the mandatory shuttle.
Best to move around a bit to enjoy these parks.
We were planning on traveling sometime in the summer months (June - August)
Brian head is the nearest ski resort but it is a very small town and doesn’t have much going on in the summer. Maybe some bike trails. Not sure. Some hiking. It’s proximity to cedar breaks makes that a nice visit.
Duck creek is nothing even close to a town but there is fishing.
Kanab is the town most central to all three and has several activities nearby- coral pink sandunes( with atv’s a possibility), close to the hikes at Paria and cottonwood wash for example. Not to mention best friends animal shelter.