Campgrounds and availability.
That will make for a nice trip over 9 days and you should have time to visit Zion NP between Bryce and Vegas. To go into Zion you will have to pay an extra fee and wait a little while to get through the Mt Carmel tunnel, but it's a great drive. This is so they can stop on coming traffic entering the tunnel from the other end so they can let larger vehicles drive down the middle of the tunnel to avoid the roof connecting with the side arch of the tunnel. It might already be too late to find RV sites inside the National Parks but it's something you should get onto straight away, sites are limited in number and big in popularity. In GC you have Mather without Hook ups or the Trailer vilage with them, both are in a good location near the village and rim. For Bryce canyon you could check out 'Rubys Inn' campground right by the entrance to the park. Nearby Ruby's has a store and dining facilities and across the street is Bryce old town. Zion's popular campground is the 'Watchman' located near the entrance to the west and the lovely town of Springdale.
In Vegas 'Circus Circus' has an RV park right on the Strip, although it's more of a parking lot. We opted for the Oasis RV resort which is pretty cool, although it's probably around a $20 cab ride these days to the Strip.