From Michigan you could take 57/55 down toward Memphis and pick up the Natchez Trace Parkway ending at Baton Rouge - lots of history and a beautiful drive. Then go to New Orleans. There are some nice state parks around New Orleans such as Fairview-Riverside or Fontainbleau. Drive into the city and book a city tour for a great overview. It's the best way to see a large city especially if you're short on time.
As far as time - for a two-week trip I'd recommend stopping at Arizona (Grand Canyon) and then head north into southern Utah for the great national parks - Zion, Bryce, Arches, Capitol Reef, Canyonlands before returning home via I-40 or I-70. Your two weeks is really a short time for that many miles.