You'd most likely find that you'll do a lot more sailing if you sail one of the large lakes closer to you.
I'm in Muskegon, Michigan and here we have the option of sailing Muskegon Lake, or Lake Michigan, depending on conditions. Lake Michigan sailing is awesome. There's plenty to like about it.
Here's why I question the idea of taking the train to a boat kept in Chicago. Weather. You're going to spend a lot of time traveling only to get to your boat and find there's no wind, too much wind, or thunderstorms. The other thing that'll happen is you'll look at the weather forecast, see that it looks a little iffy, and not go. Only to find out later that between 11a.m. and 8:00pm the sailing was perfect. And you missed it.
Sure, we take our Catalina 28 north, and visit other ports for vacations. That's a lot of fun. I've been doing that my whole life, and is why I now live next door to the marina. However, most of the time, we daysail. Back out of the slip, make a beeline for the channel to Lake Michigan, then sail ten miles out and ten miles back. Return to slip. How is that different from sailing in circles? Not much.
If you want to experience the Lake Michigan thing, PM me and get yourself up to Muskegon and I'll get you out for the day on Straycat.