If you want to do some semi-urban riding you could try the University of Windsor campus. There's also a riverside pathway (smooth concrete, about five feet wide in each lane) that is mixed use (runners, roller bladers, cyclists, etc.), although I'm not sure how fast you'd be able to go. Riverside Drive might be a better option for going fast, but since it is a two lane road laced with many curves and bends located in a city where people are unaccustomed to bikes...maybe not.
If you're looking for trails or paths through parks there is the Ganatchio (sp?...pronounced Ga-nacho) Trail which is way on the other side of town (20 minute drive in a car).
Hope that helps. I grew up there but didn't get into cycling until I moved to Toronto.
I agree with the above statement - I grew up in Tecumseh, just outside of Windsor to the East, and the drivers there have always been ridiculous. The Ganatchio trail is a very nice ride, and I think that its been extended somewhat recently, so you're able to travel all the way from the Ambassador bridge into my home town that I mentioned a second ago. That's usually ~45 mins if you keep a good pace. But its very flat.
If I were you, I'd look into some of the townships around Windsor to find some rural country road. Lasalle, Amhestburg, and even Leamington would be some places to look into. Keep this thread alive, because I visit relatives there frequently and I'd like to find some routes as well.
I know it's too late for the original poster, but for anyone else looking to ride near Windsor a friend was just telling me about the good riding available on the Greenlink Trail. It's an old reclaimed railbed that runs from just outside Windsor through the county, at least as far as Harrow. You can pick it up on highway 3 just off of Walker Road. Apparently there's an old fire station there where you can park your vehicle.