The Toledo Art Museum is free and offer kids activities on certain days. The Toledo Zoo is awesome, definitely worth purchasing a season pass. Along Route 2 near Port Clinton, there's a drive-through safari and a deer petting zoo.
Fort Wayne Children's Zoo is one of the 10 best zoos in the USA, you can feed the giraffes there...Fort Wayne also has a science museum.
In Ann Arbor, our favorite place is the UM's Matthaei Botanical Garden, which is free to the public every Friday afternoon. Outside Ann Arbor, there's the SASHA Wildlife Sanctuary in Manchester, MI.
The Huron-Clinton Metroparks in SE Mich are awesome ($20 for an annual pass). Right off I-275 one metropark offers the Turtle Cove outdoor waterpark.
Oh, another favorite of ours off I-275 is Calder Dairy Farm in Carleton, MI. We went there last year with my mother's group and my older son got to take a turn milking a cow as part of the farm tour. He's been begging me to go back. You can schedule a group tour for about $7 per kid, including a wagon ride, milking a cow & ice cream at the end of the tour.
Hmmm...we have lots of other favorite field trips, but now I'm drawing a blank!