One of your first stops should be River Raisin National Battlefield Park Visitor Center. Here, you'll be able to find your bearings and get lots of useful information before you start exploring.
You'll have sightseeing choices galore when visiting Monroe. River Raisin National Battlefield Park Visitor Center is an ideal place to begin here, but there are many other interesting sights to visit. The Mall of Monroe, William C. Sterling State Park, and Raisin River Golf Course are not far from the tourist information center and will fill in your day nicely.