Yes you can swim in the water. You will find more people swiming at the beaches west of town where the beaches are nicer.
This year may be an exception, but most years the water in the Straits of Mackinac stays colder than most people from farther south want. Young people usually mind the temperature less. I grew up in Mackinaw City and spent a lot of time in the water as a child, but as an adult, I like the heated pools.
The beaches change year to year, so I can't be say which ones will be the best this year.
Things to do include Mackinac Island, Colonial Fort Michilimackinac, Historic Mill Creek Discovery Park, Old Mackinac Point Lighthouse, Mackinaw Parasailing, cruises on the Ugly Anne, lighthouse cruises, Jack Pine Lumberjack Shows, Icebreaker Mackinaw Maritime Museum (very neat), Thunder Falls Water Park, mini golf, hiking and free concerts at Conkling Heritage Park. There is bicycling on smooth trails or mountain style.
Your teens would probably enjoy tubing or canoing with Big Bear Adventures at Indian RIver.
I would also day trip to the Soo Locks and Tahquamenon Falls in the eastern Upper Penninsula.
Edited: 31 May 2012, 12:40