Egg patterns take a ton of fish, as do nymphs, caddis, and smaller speys.
If you go to the Big Man try to avoid Tippy dam, that place is loaded with liners/snaggers. Those guys rip and strip the salmon like mad.
Wellston (on the Big Man) has a great flyshop, the owner is very concerned about the fish and fishermans ethics. Please PM or e-mail if you need contact info up there.
The Betsie is nice but can be crowded at times especially around the Homestead dam. Grab a DeLorme and do some exploring.
Nice thing about many Michigan rivers is that you can access water running thru land that is posted no tresspassing. You have to keep your feet wet to do it.
If you are avoiding fishing thru pods of fish and fishing the darker water behind them you will legally hook more fish then you can handle. Timing is the key part, after a good spate of rain is your best bet for latching onto some stud fish.
Enjoy yourself and please post the results of your trip.