We stayed at this campground last week. It is a very rustic campground with about 13 sites. which are first come first served. Here is an info link Elk Fork.

It is located on US 14/16/20 which is the road from Cody to Yellowstone (south entrance). It is about 30 miles from Cody and maybe 20 miles from Yellowstone. Across the road is the larger Wapiti campground. Elk Fork does not have water available ... you can can get that at Wapiti though. There are vault toilets. Each campsite has a bear box, fire ring and picnic table. There are a lot of very nice hiking trails nearby. The cost was $10 per night. Although very rustic, this was my kids favorite campsite of our yellowstone trip.

View of the campground from about 400' up