http://www.dcmm.org/ The Maritime Museum in Sturgeon Bay is very nice and open year round.

You can do a Door County loop drive stopping along the way at the sights to see. Peninsula State Park is a good one you can find walks of varying degrees. Whitefish Dunes State Park has some hikes or just walk along the beach. Next door is Cave Point and although you won't be climbing down there it's a pretty spot. I haven't visited these in Fall but I'm sure they're still beautiful, just a different season.

Check www.doorcounty.com for maps and places you might be interested in. It might be fun to just be spontaneous and drive and stop as you please. It's so versatile in the Door as we aren't talking huge distances between places. There's state parks, parks and many stops along the way to stop at. Even if rigorous walks aren't out you can hop out and lightly peruse each of the areas or the ones you find most appealing.

You have Potawatomi State Park right in Sturgeon Bay. You can find and enjoy that area, or branch out and explore, all depending on what you feel you're up to. Again driving can be a big part and you'll still see/enjoy things that way too.