Check out 1300 Lafayette. They are co-ops but you can rent if you are seriously thinking of buying. We are 5 min from Greektown. We have 2 pools, a gym, 24 hour security.
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The Jeffersonian is excellent for newbies, too, btw.
http://detroitmidtown.com/05/midtown.php
This site has a bunch of rentals listed. I don't know if they're all up to date but it could give you an idea of what's available.
I've lived in Rosedale Park for years, and it is a great family-oriented neighborhood. It is also very walkable, with just about anything you want located right in the neighborhood. There is a neighborhood-wide openhouse coming up in early May, I think. http://portal.rosedalepark.org/
The Community Development Corporation in this neighborhood is Grandmont-Rosedale Development Corp. www.grdc.org