Here is a map for our area I found from the Michigan DNR, other areas are also available on that link. Streams and lakes highlighted are for trout, click on the DNR link above for more information.
All of these areas are less than an hour's drive from Birch Lodge, most are about 30 minutes.
In addition, beginning April 1, 2013, the Michigan DNR is employing an experimental increase in the daily limit of brook trout in several streams in Michigan. This would double the daily limit from 5 to 10 in 2013. One of these streams is the Eastern Branch of the Tahquamenon River. Basically, this experimental area pertains to the waters upstream from the bridge on M 123 north of Eckerman MI.
Eckerman, MI is 11 miles north of Birch Lodge, Trout Lake, MI on M 123.
Although we won't be open to put you up in April, I hope this will give you something use for planing your trip to the U.P. In the meantime, you can dream about all those fish!