I've stayed at Elkmont many times. It's about 7 hours from my house, so know the miles are worth it. For those that can do without electricity and onsite water and sewer, this is the best campground in the Smokies. All others have a dump site in the campground. The closest to Elkmont to dump RV tanks is across from the Sugarlands Visitor Center almost 7 miles away. I wish Elkmont would remedy that, but it stays full most of the camping season as it is, so I doubt any upgrades are forthcoming. It's the only thing keeping me from giving it 5 stars.
That aside, this campground is our favorite. The Little River that flows through the campground is great. It's good for tubing. The campground store is well stocked most of the time. There aren't as many ranger led programs as there used to be, but the one's still there are wonderful.
The circus that happens during the firefly event is also worth putting up with. There is nothing like the display the fireflies put on usually the first 2 weeks in June. Keep in mind reservations for that week must be made pretty soon to the 6 month period the NP set up. Wait a month and you won't get those weeks.
Lastly the weather, although this area receives the 2nd most rainfall in the lower 48, is very cool in the dead of summer. Might get hot in the middle of the day on rare occasions (good time to dip into the aforementioned river that never gets too much above 40 degrees), the nights are usually cool enough to sit around a campfire.
The "month visited" down the menu would only give me one choice. July is the last visit we made, but any month its open is great. Again if you want the firefly weeks or leaf peeping fall weeks, make sure to reserve right at that 6 month window. Or you will have few choices if any.