How far away is acceptable? I'm not aware of any in Elkhorn itself, but there are a couple Wisconsin SF CGs not too far away: Ottawa Lake (Kettle Moraine South) in Eagle, and Bong SRA in Kansasville. Also check Lake Geneva and Delavan for CGs. (Personally, I don't recommend Bigfoot Beach SP in Lake Geneva.) We've been to both the SF's I mentioned & like both. Electric hookups, showerhouses, dump stations. Reservations WILL BE NEEDED for weekends in both parks, and it's possible all the electric sites will be booked for many weekends during the summer.
Ottawa Lake State Park is a very nice place about 30 minutes from Elkhorn. They do have some nonreserveble sites but they fill up real fast on weekends, sometimes by Thursday. Here's a link:
I think there is camping at the Walworth COunty Fairgrounds just outside of town. Not sure if it is available to the "public" or just for events, but they have a nice area with trees and so on...google it up. It is right in Elkhorn. I will be camping there soon for a dog show at the fairgrounds.