Mid to late Sept is a good time. The weather is mild and more important, the kids are back in school so you can really enjoy the park and the town. Any of the RV parks are going to be good and there are enough day trip possibilities to keep you rolling for a week or more. Spend some time in town and go to Tom Till's photo gallery, you'll leave amazed.He has spent years photographing the Southwest. If you are a photographer, take a good photo guide, it's a photographer's paradise. There are many on Amazon, but the best ones are by a French guy named Laurentz Martres' or something like that. Just Google Photographing the Southwest.
You may want to consider making the big loop that includes National Parks as well as some state parks and ends at Zion.