Before you get to Bryce NP, on Rt 12, there is a campground called Red Canyon (Dixie) which is one of my favorites out of the 2,400 we've been to. Why? Besides the amazing scenery all around, the hiking trails are super (Golden Wall trail would be challenge for you teenage boys while Buckhorn is great for an after dinner hike). FYI: Red Canyon cg has hot showers and a dump station and is in the heart of Butch Cassidy's stomping grounds. A visit center to the Dixie National Forest is also suggested (on the left before the cgs).
I assume from the South Rim you'll be taking Rt. 89. Have you considered taking Rt 89A rather than staying on Rt 89 going through Page, AZ? It is a breath-taking drive. Make a stop at the Trading Post at Cameron, AZ (on RT 89) than pause at one of the Native American run roadside stands. Interesting contrast.
If they don't have them already, you might consider getting your boys their own cameras. It would be a good way to keep them interested and provide a way for the whole family to remember this trip.
In my opinion, Zion NP is way better than Bryce. That opinion is based on the hiking trails. Zion is where I learned about the effects of elevation on cooking . Took almost a half-an-hour to prepare canned hash and eggs for dinner - good memories. And you'll have a bunch from your travels too. Enjoy and if you want details about Red Canyon cg check forestcamping.com.