Neat little trailer! Congratulations and welcome!
You have hit on the one thing that takes both a bit of research and trial and error. As time goes on you'll know what to look for in a campground and be able to find those types of places easier. We've always been partial to state parks, but in WI they are very hard to get into because they are so popular. So we've found a few private places that are to our liking. but even with reading reviews, you still have to try and see.
2013 Jayco Jayfeather X20 E, 2008 GMC Sierra 1500 Crew Cab Z71 SLE