We have two dogs and needed air conditioning running in the Safari when we left them behind to go into the park. We were there in mid-May and it was warm enough to need that (and we got snowed on once -- go figger...). Therefore we stayed at Ruby's Inn campground -- absolutely the cleanest bathrooms/showers ever! Laundry was nice. And yes, the folks were very accommodating. In mid-May we had reservations and they were full on 2 of the 3 nights we were there.
Campgrounds in the park looked nice if you don't need electric. About the only grocery store in the area is Tropic IIRC. Or Panguitch. There's a small convenience store at Ruby's Inn lodge.
Red Canyon is a nice base about a dozen miles down the road; there's a forest service campground or Red Canyon RV Park
. One of our members reported running into a bunch of rowdy ATV-ers at Kodachrome Basin campground -- a variable observation at best.
The shuttle service in the park is easy to use. Unlike Zion, you can take your car all the way to the end ... stopping at overlooks as you do. At the NPS booth next to Ruby's Inn campground office or in the park at the visitor center -- do make a reservation for next day to take the guided shuttle trip out to Rainbow Point. The bus driver narration is very useful and we got a side story on all the local Butch and Sundance lore.
Please post back here about how you dealt with accommodations.