The beaches in that area aren't great to be honest. There's Bay City State Recreation Area which is about as good as it gets, but Saginaw Bay shoreline is more wetland/mucky than it is beachy. If you want to drive an hour north of there you can find some nice shoreline.
The best beaches in Michigan, however, are on the west side of the state on Lake Michigan. Saugatuck, for example, is awesome.
Wow, you're going to be about 20 miles from here.
There are no good beaches in Bay City, because its an industrial town and the Saginaw River dumps in there, with effluent from Dow, and General Motors upstream.
There is a decent beach up at Tawas, which is less than an hour north on Lake Huron.