You can dry camp in downtown Chicago. NO FACILITIES. McCormick Place, a large convention center just south of the city, has a large parking lot where overnight parking is allowed. It's a commercial parking lot with lots of tractor trailer traffic, but if you park on the north end of the lot with the other RV and tour busses it's pretty quiet, again considering it is a commercial parking lot. No problem running your generator all day and you will have plenty of space to park.
It's not particularly pretty, but it is safe with security patrolling the lot regularly. It is a $11 uber to the north end of Michigan Avenue, so probably half that to the south part of the city near Millenium Park and the museums. You're also within easy walking distance of the lake and the bike/walking trails that extend for miles and miles in each direction along the lakeshore.
Don't have the links handy, but just google RV and motorcoach parking McCormick place and it should pop up. I think it runs around $35/day.