Signal Mountain or Gros Ventre Campground?

We are planning on 3rd week in June for GTNP, Colter Bay is booked for the days we are planning at this time. We have not stayed there except for tents way back in the -- well many decades ago. We now have a 30' fiver so we had wanted to make sure we had a reservation. I will keep calling to see if something opens up, other wise we will just look around when we get there. Should be fun!