Kayak on the Detroit River
This is a good idea, for obvious reasons, such as, ya know, being surrounded by water. You can bring your own kayak, if you happen to be stowing one away, or rent one right from the main beach. Check out RKC Adventures, which also organizes tours of Belle Isle’s lagoons and canals. Plus, even though it's considered "exercise," you're still sitting down.
Bike around the island
Pedal the 5.5-mile loop around the park, and if you’ve got beefy enough tires, you can venture off into the forest for a bit of off-roading. Make the most of your day and take advantage of Detroit’s often-empty streets by biking to the island and back -- completely avoiding the $11 state park entrance fee.