Best option in Oshkosh
All the other campgrounds in OshKosh are near the airport, which makes sense since the biggest event each year is the EVAA air show. None of them have trees.
Hickory Oaks has it's own airfield and lots and lots of trees. They even have a mini-lake (4 acres).
There are all types of RV sites, tenting/primitive sites and group sites, some small cabins as well. We camped in site 60 because we arrived after dark, and Cindy suggested that our first choice, #67 might be too hard to find at night. There is only one street light, and it's by site #1 and the swim area.
The map doesn't really convey what an oasis of trees this place is. To the West is the runway and beyond that, a large grassy hill (it's actually landfill). To the east in a rural road running along the lake. To the north, in the distance is a prison. That all sounds worse than it is, it's a lovely campground.
There are a few things for sale in the office, but you're so close to town you can get everything there. Cindy the operator is extremely nice and helpful.
Fire pits are 30" rings with no grate, Tables seem smaller than average.
If you're visiting in the summer, be sure to visit the Farmer's Market , Saturdays on Main Street, also Wagner's Market for the best meats, deli and beverages. The Paine museum & gardens and the city museum are both worth visits as well.