Hi,
I was there around July 4th in 2006, and did not find any 'open' spaces to park in, but I was able to get a reservation for 2 nights at one of the 4 or 5 campgrounds inside the park. Yes they can fill up fast. It is not like my 1994 visit where if you selected a campground before 10 or 11 am, you got a site without a reservation.
I did not have a schedule to keep, and was able to park outside Yellowstone along the river in a designated free camping area in 2006 (however they where installing a pay post as I was camping there to start charging people to park in this dirt area next to the road with marked camping areas). I love dry camping, and have a 400 watt solar system, 100 gallon fresh water tank, and don't like campgrounds that much.
But in Yellowstone, along with all National Parks, you don't have a lot of camping locations to pick from, and 50,000,000 campers trying to go there. I would get the reservations, and then if you are out sightseeing and decide to use another campsite for 1 night, get that one too! And you can finish your 5 nights at Fishing Bridge. While $54 a night might seem pretty steep, it is the only campground there with electrical hookups, and also they spent a huge amount of money a few years ago to upgrade everything in that campground. It really is less than a tank of gas in a modern RV or pickup too.
If you are willing to 'chance it' and I was, then no reservations will work out fine. It did for me, as I was able to drive into the park in my towed vehicle, look around, and camp along the Yellowstone River near Livingston, then get my reservations for the south half of the park later in the week, and stay there a couple of nights, as I made my way to Jackson Hole NP. There I also dry camped in a place that I had found in 1994, along the Snake River (where you can jump across it because it is only about 6' wide) just west of Flagg Ranch. Flagg Ranch is a huge campground, with a few hundred sites.
Jackson Hole and Yellowstone NP are only a couple of miles apart, and Flagg Ranch is located between the parks. Not much worry about getting a site there.
For anyone who can not get a site in Yellowstone, there are a few other places to spend the night. West Yellowstone is the closest place with full hookup campgrounds other than Fishing Bridge inside the park. All the other Yellowstone campgrounds where dry camping when I was there in 2006. North of the park is Livingston, and several places where you can camp along the river, enough for about 100 RV's combined, but in several locations. Livingston has a nice laundrymat, and if you take I90 west a few miles there is a Wal Mart where the park workers can find reasonably priced food. Food trucked into the park is expensive!
I was always adaptable about where I would park for the night. I did not mind finding a wide spot on a fire road, and park out of the way. Be adaptable to what is happening, and you should enjoy the vacation!
Have fun on your camping trip!
Fred.
