Depending on which side of Dundee you are in there is Memorial park and Elmwood Park pretty close that have good paths for running. they are next to UNO's campus. When I lived in the area I loved running through the neighborhood, the houses beautiful there.
I am not sure about bike paths or rentals. But Bike Masters and The Bike Rack would both be a good place to start. If they do not rent bikes themselves, they would know places that do. Also they would have great information about paths.
ITA that Memorial and Elmwood Parks are beautiful places to run... Near Elmwood Park is the new Blue Cross Blue Shield HQ, and they have bikes for rent (kind of like the stroller rental at the malls).
At any of the bike shops, you can pick up a biking/running trail map. Olympia Cycle is the closest bike shop to Dundee. Another option is Greenstreet Cycles downtown. I don't know about bike rentals.