We have stayed at Fishing Bridge, inside the park. They will accommodate up to a 40' rig + vehicle but you MUST have reservations. The spaces are fine length wise but close together width wise. They were originally designed for trailers pulled by cars. Most people who stay in Fishing Bridge are off running around the park so you don't set up camp so to speak because by the time you get back to your rig you are exhausted.
You are not allowed to have food or anything like that outside unattended because it is frequented by bears and bison. We stayed for 5 days and LOVED the close proximity to everything within the park. We went to every entrance and all the way down to the Grand Tetons. Here is a picture of our rig in a slightly smaller space (when we set the reservations we had a smaller travel trailer and bought the new rig three days before we left for the trip):
Here is picture that shows you the width of the sites:
Here is a picture of our rig from the other side:
This site is not for everyone but we LOVED it! Just make sure you arrive during the day so you can find your way around because it is NOT well lit and there are lots of trees. Huge SOBs use this site and do not have any issues. We have also heard great things about Grizzly RV Park outside of YNP. No matter where you stay you will REALLY ENJOY Yellowstone! It is truly amazing! Feel free to PM me with any questions you have as we only live a few hours away and visit fairly regularly. In fact we have reservations for the end of May through the first week in June. We are going to change our reservations a little and go around June 1st or there abouts. AS for weather it could snow or be in the 70s. So be prepared for anything and you will have a great time! Make sure to bring binoculars and a spotting scope if you have it!Have fun!