Last year, we visited both parks, and I highly recommend Headwaters Lodge at Flagg Ranch RV Park. It has full hook ups and is a very scenic area. It is centrally located between Grand Teton and Yellowstone. You are only two miles from the south entrance to Yellowstone, and a short drive from Jackson lake. There is a ton of wildlife in the area too. The lodge has a nice restaurant, and they also have gas and diesel pumps. Here's a link to their site:
Headwaters Lodge at Flagg Ranch RV Park.Please note that when you purchase your entrance fee to Yellowstone and Grand Teton, you can get a combined pass for ten days that will cost you $50. Or, you can spend $80 and get an access pass that is good for all national parks for a year. Of course, if you are 62 or older, you can get a permanent pass for a very modest fee.
Jim