There are well over a hundred nice RV parks/Campgrounds in Southern West Michigan especially near the lakeshore area which would meet the OP's wants. Yes, they are popular too and fill up or are booked so reservations are very strongly recommended or a must. They are within 2 to 2-1/2 hours of Chicago with normal type driving but of course it depends on where in the Chicago area the OP lives. The Chicago area is a gigantic concentration of choked traffic much of every day because there's over 10 million people and 1-1/2 sides of the metro area is blocked by Lake Michigan.
If the OP lives on the north side, it can easily take 1-1/2 to 2 hours of bumper to bumper stop and go driving just to get thru the Chicago area going east toward Southern Michigan. Vice versa if the op lives on the south side and goes north thru the Chicago area. Truck traffic is INSANE as it's the min east/west truck route across the USA for deliveries to over 100 million population! Chicago desperately needs another 1 or 2 major many lane interstates etc going across the south side east and west.
Us living in West Michigan on the lakeshore, we always avoid the Chicago area like the plague when going SW or W when in or towing an RV as we'd done it way too many times (dozens+) before and it's NOT fun! Much more pleasant and often faster for us to go thru the Upper Peninsula of Michigan.
Therefore, you can't go Northeast, east, or southeast from Chicago unless you first go south around the bottom of the huge Lake Michigan and that creates a gridlock of a traffic jam with all the other vehicles and truck especially on Fridays and Sundays as so many are always leaving on Friday and return on Sunday.
Not much of what the OP wants is 2 to 2-1/2 hours driving an RV west or south of Chicago and going north has Milwaukee and the other lakeshore cities with their residents wanting much of the same as the OP but not enough places for all of them RV to. Only the OP knows where in the Chicago area he lives and what that means. My Dad was born in Chicago and I have lots of family still living there we visit so I'm/we're no strangers to the Chicago area.
RV'ing and camping is extremely popular in Michigan and is why there are several thousand CG's in the state. We are now in our 53rd year of RV'ing in the State of Michigan where we live.
