Lake Michigan is a ways from Appleton, but Appleton is on Lake Winnebago--a very large freshwater lake. Large enough that the wet suit might be appropriate.

Swimming in Lake Michigan? Definitely wet suit swimming as the water temp rarely reaches 70. Eons ago when I was younger, fitter, and dumber I swam every day off Milwaukee's Grant Park without a wet suit. I'm not sure I'd try that now.

However, another cycling/hiking thought to consider is to hit the Kettle Morraine State Forest. It is off the direct path from Chicago to Appleton to the east, but is lovely. Good biking and really good hiking. The Ice Age trail (Wisconsin's dream of a long distance hiking path) is pretty complete through that area. The trail follows the distal edge of the last glacier. In some areas the trail is nothing more than recovered rail bed ( e.g., from southern Door County south ), but inside the Kettle Morraine area it is rolling (up the morraine and down into the kettle; up the morraine and down to the kettle....lather rinse repeat).

If interested, let me know--we've hiked a lot of that area and we can point you to some of the prettier areas. Likewise cycling routes.