H E R E - Trailer Village is the place to be, for what you're looking for. Inside the park, full hookups, within walking distance to shops and restaurants, and a shuttle stop at the entrance to get you any place you want to go in the South Rim area. Park and forget about having to drive anywhere. Shuttle can do it and there's no charge.
Make reservations as soon as you have a firm date of arrival, and do that as soon as possible, to make reservations NOW so you're more likely to get spaces that are in close proximity.
Thanks for the info. My next question is...are there plenty of things do if we stay for a week or are we going to be bored after 2 or 3 days? Trying to decide if we want to stay a week there or stay a few days and then move on to a different location like Bryce National Park.