I'm trying to keep from pointing and laughing.
You do realize, I hope, that Yellowstone is the most visited National Park in the entire US, and July/August are the height of busy season. Reservations or blind dumb luck are the only way to get into any accommodations in the park, and reservations fill up 100% months in advance. But you might catch a cancellation. Finally, dogs are pretty much not welcome anywhere in the park, so you'll have to keep it on a short leash.
The only campground in Yellowstone that has ANY hookups in Yellowstone is at Fishing Bridge. You might consider trying the campground at Flagg Ranch, which is the northernmost campground in Grand Tetons NP, but is only 6 miles outside the southern gate of Yellowstone. When we were there a year ago in June, it had just reopened after being closed for a while for renovations. They may have some openings, and that's pretty close. Go for it, check the Yellowstone reservation system, it is possible you'll get lucky. But do not count on being able to have your pick of multiple open sites.
