I refuse to answer that question on the advice of my attorney.
Would you recommend going to Yellowstone or Glacier?
What follows is probably more info than you want, but you asked
Zion is right next to the town of Springdale, a small town with a lot of h/motels and restaurants - limited lodging in the park. Great short hikes
Bryce has the same issue with limited lodging in the park and about the only thing nearby is Ruby's. Again great short hikes.
GC is grand! A lot more lodging in the park . . . the adjacent town is a bit of a drive and the toll booth gets congested. The trails are longer if you want to get to the good spots.
Zion and GC (west end of south rim - the major tourist spot) are carless with frequent shuttle service. I'm not certain about Bryce. I have only visited these parks in "value" season, but I suspect July is busy, so make ressies soon!
Zion is easily accessible from the north-south interstate (I15?). It's not far from Bryce . . . the road out of Zion heading to Bryce is spectacular. The first part is windy - up over and thought the mountain! Once you hit the main north-south road on the east it's much straighter whether heading off to the GC or to Bryce. GC to Bryce/Zion will not be a bad drive and you will go by the Glen Canyon Dam.
As I recall, the mapquest travel times are fairly accurate (unless you stop and sightsee. Also, if you do Bryce/Zion, it's easier to combine them with north rim rather than south rim of GC. The down side is there isn't much lodging nearby . . .
It's not hard to get between the interstate and Bryce without going through Zion - the roads that show on the maps are fine. The same for North Rim GC. Just limited services.