Lake will likely be 68-70 that time of year, but Lake Michigan is prone to dramatic temperature changes - the water will "roll over" and an under layer of cold water will come up and it drops unto the mid-60s or high 50s. So odds are very good it will be swimmable but you could get a cold day or two. We have rented places in August on Lake Michigan all over the west coast of the LP and we have always spent a lot of time in the water. But it will never be super warm like the Gulf or Caribbean. Air temps should be plenty summery and it will likely cool off a little at night (sweatshirt for a s'mores bonfire on the beach, for example).

There are lots of great places to stay. For the best of both worlds - maybe find a rental on an inland lake and then hit the beaches on the big lake. We rented a place called Sleeping Bear Cottage last fall for my inlaws 70th birthday that was on a tiny lake (Little Traverse, maybe) right between Glen Arbor and Leland, super close to the dunes, and with a path through the woods to the big lake (about a mile). Came with kayaks, sailboat, paddle board, little dock with fishing equipment etc. Glen Lake and Lake Leelanau are also really nice inland lakes.

I personally like west coast on the Leelanau Penninsula better than Grand Traverse Bay or Little Traverse Bay, but all those areas have quaint towns and plenty to do in the summer.

Beaches downstate a bit are also great - Montague, Manistee, Grand Haven, Saugatuck, Union Pier etc, but the closer you get to Chicago the more Chicagoans you find (we are, but it does change the dynamic) and the quaintness of the towns is less genuine and more contrived IMO. Up north is really now as it has been for ages - it's a fun place to try for a change fo pace.