The drive from Metro airport to Mackinac is at least 4 hours, possibly more.
 
There are airports closer to Mackinac. See list below (I've never used these, before, and therefore I'm not endorsing one over another). This comes off the Mackinac Parks travel links website. It looks like Pellston has a Mackinaw Shuttle.
    Pellston Michigan Regional Airport
    Northwest Airlink (Pellston)
    Great Lakes Air Inc.
    Mackinac Island Airport
http://www.mackinacparks.org/parks/travel-links_141/
 
I think the most common place to fly in is Pellston.
 
Good luck! and enjoy Mackinaw City and Mackinac Island... don't forget to buy some fudge!
 
-Anne

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