I'm originally from Windsor so a trip to Devonshire Mall might be worthwhile. You'll find different stores, but you will need a car unless you take the Tunnel Bus across the border. Then, you'll need to take a bus or cab to the mall. Honestly, I haven't been home for 8 years (except to visit my family every year), but seriously, you will need a car to get to any of the malls in the suburbs, especially if you're staying by Tiger Stadium. Windsor has some nice parks down by the river, and there is an outlet mall, but it's nowhere near downtown. Downtown does have some shopping, but it's mostly bars and restaurants.
If you want to hit some of the malls like others have mentioned, there are quite a few. Dearborn, which is a tad closer to where you're staying has a mall - Fairlane Towne Center, and 12 Oaks Mall has always been my favorite - is in Novi, further away.
I used to use the PeopleMover a lot when I was in my 20's, and Greektown was a lot of fun, as well as Trapper's Alley.
You might want to check out the Michigan Tourism site and see if you can get more information as far as renting a car. It's easy to get lost if you don't know where you're going - especially with construction (which always seems to be going on)