Right out side Lake Geneva is some great road biking, with gentle dairyland hills and back roads if you know where to look. The sweet spot is between Elkhorn – Burington- and Lyons township, riding around Lake Geneva sucks; two lane heavy trafficked roads with lots of ingress drives and no shoulders. For mountain biking go to the Kettle Moraine John Muir trails.
For hiking the Linn Nature Park is 4 miles away, 200 acres of restored prairie for hiking. The White River County Park is awesome; 210 acres with 2 miles of the White river, for kayaking in the spring. Both are dog friendly.
Further from town the Kettle Moraine state forest and LuLu Lake and Crooked Creak Preserves. Just ask Google.
Outdoor Wisconsin, gotta love it.