Since you have this "reverse" idea in your head, I am assuming you are talking about going north in a RV, since folks with homes at both ends of the trip don't call it reverse, it is just snowbirding. North in the summer, south in the winter, whether you do it RV or sticks and bricks, ownership or rental, migrating makes you a snowbird.
I know the Great Lakes area. Camping seasons range from beginning or end of May to just after Labor Day in some places, end of October at the latest. Memorial Day through Labor Day, most places you might want to go will be quite busy, if it is on the water, and most places will be on the water in Minnesota, Wisconsin or Michigan. Busy means expensive. To get away from that, you need to get beyond a full day's drive from major metro areas like SE Michigan, Chicago-Milwaukee, or Minneapolis-St Paul.
One of the nicest long-stay resorts is Petosky Motorcoach Resort near the tip of the Michigan Lower Peninsula. This one is an ownership resort, but owners rent out their lots seasonally as well. To find out what it costs, you have to call or pretend to book.
Closer to the busy summer resort area of Traverse City, the nicest place is probably Traverse Bay RV Resort. Lots here are currently selling for about $65,000, which is actually pretty cheap for a piece of land that size anywhere near Traverse City. A little more downscale, Holiday Park on Silver Lake (about 10 miles out of Traverse City) rents sites at $50 to $75 a night, the lower cost sites going for about $300 a week for longer stays. You will find similar rates in other parks/resorts in Benzie County (Frankfort, Benzonia) unless you want to be actually on the Lake Michigan shore, on Crystal Lake, or close to the Sleeping Bear Dunes.
Prices should be lower in the NE part of the LP (from I-75 over to Lake Huron) but I can't vouch for any places because I always went to the NW part. Upper Peninsula will be a bit less expensive, if you get away from the extremely popular straits area (e.g. near St Ignace). Still, for decent parks with long term stays, and near cities (like Marquette, Houghton or Escanaba) you'll be looking at $40 a day or higher. Town and cities in the UP often have small public tourist parks in the $20-30 price range, but most of these have limited stays, often 14 days, sometimes less.
For Michigan, you don't want to be any further south than Houghton Lake, where the summer resort area starts, unless actually on the shore of one of the Great Lakes. The summer climate is still central plains, and temperatures can reach the high 80s regularly, into the 90s from time to time. Corresponding areas of Wisconsin are north of Green Bay (the Door Peninsula is really nice in summer, but just as popular and expensive as Traverse City). For Minnesota, up in the Thousand Lakes area north of Minneapolis.
One more thing to think about, June through August is severe weather season for the Great Lakes, with thunderstorms as warm and cold air masses push at each other, occasional tornadoes and more frequently straight wind speeds that will challenge RVs.
