Er, yeah. June is pretty much the only month of the year that I actively avoid the woods. With the wet spring the area has had, my prediction is that you will be eaten alive by mosquitos and biting flies. Have you seen King Kong? Remember the bug scene? That’s what it’s like.
That said, bummer on the Apostle Island trip. That sounds like it could be a blast.
If you’re determined to be bug food in June, consider da UP! Definitely within an 8 hour drive of Lacrosse, and there’s everything you asked for. It’s also a lot less of a tourist destination than northern Wisconsin, which means you’ll have a lot of space to yourself, and the prices may be slightly less. In general, it’s more rustic than WI, less farms and more forest.
In Marquette county, you can easily car-camp either in designated campsites or just pull off on one of the gazillion dirt roads. The terrain is up and down, downright rugged in places and rarely flat. You can do day hikes where you get a 360 panorama of the whole area.
Bike Magazine has rated the area as one of the best mountain biking areas in the country on several occasions. The local bike shops can give you trail maps.
Kayaking Lake Superior is gorgeous. You can put in at secluded beaches, or you can paddle into some spectacular scenery right from town. I’m talking 60-70 foot cliffs and sea caves.
Farther east from Marquette is Pictured Rocks National Lakeshore. Same thing there as far as camping, hiking, and kayaking, only more of it. West of us is Porcupine Mountains, which I’ve never been to but have heard is really great.
Downwind Sports is a local sports shop that specializes in hiking, biking and kayaking. They’re pretty friendly and if you give them a call or check out their website they can point you to specific hikes, rides, or paddles that you might like. There are also local biking and paddling groups in the area that they can hook you up with if you want company from the locals - there’s a ton of trails here that are completely undocumented and you’ll never find on your own, but go along on a ride and you’ll get a good dose of them.
Same with the kayaking, although there’s a safety aspect with it as well. Lake Superior can be dangerous, especially to a lone paddler.