In Evanston at least, after labor day any of the public beaches can be sailed because lifeguards are gone. I've sailed Gillson beach in Winnetka after labor day. Waves and chop are dependent on direction and wind strength.
On a north to northeast wind, Greenwood Beach in Evanston can be sailed by a sailor who cannot waterstart at up to 15 knots, and it will be variably wavy depending on when the wind started. It can be fairly flat for the initial several hours. The wind is usually very steady. It's totally safe to try to sail, the waves are right on shore, if you are able to uphaul and sail out successfully, you can uphaul and sail back successfully. Try a small distance out initially, then longer as you get comfortable. You get washed back to shore. It's a very long beach that you can launch way upwind and give yourself a lot of beach to get back in, there are 2 beaches southward for a true swim-in emergency. Don't try it on days with a small craft advisory. If you are willing to sail 6 knots at an inland lake, the big lake is sailable at 6 knots on a north wind. Above 15 knots, Greenwood is for waterstart/footstrap sailors.
On SE to SW winds, Greenwood or the next beach south Lee Street are sailable, direction goes from sideshore to side off-shore, and these sites vary from flat water to choppy depending on the wind strength and direction. It's not hard to uphaul no matter how strong the wind is. The more west the direction, the flatter the water, but the offshore direction is more severe and the wind tends to be further away from the launch (you head south out of sight from the launch). You want to be confident working your way back upwind, with a daggerboard it will be a piece of cake in light wind, the risk is if the wind is stronger than you can handle and you get blown downwind. The wind tends to get better the farther south you go, it's not very good when you are in sight of the launch, so confidence is needed to enjoy these directions. Use a board with daggerboard initially.
On a NW wind, Gillson beach is perfectly sideshore and a long beach. Chop will vary depending on wind strength, probably very easy to sail up to 15 knots.
Straight E or W avoid Lake Michigan.
Rig small if you are worried about too strong wind. Test your ability to uphaul in the conditions, don't use a 9.5 sail unless its perfectly flat.
They teach beginning windsurfing at Northwestern Sailing Club, often see beginners sailing out of there in all wind directions (they have a rescue boat though) on light days.