K.,
I am from Michigan and have gone to Mackinac a number of times (in fact I got engaged there). We usually stay at the Island House. We have always gotten decent rates there. If you are worried about the cost, it is much cheaper to stay off the island, so you may want to stay on the island for one night for the experience and then the other nights stay off the island and take the ferry over. There are tons of hotels, restaurants, etc. in Mackinaw City (including an Italian restaurant with a Mackinaw Bridge museum in it that would be neat to take your kids to) and it is much cheaper. There is also a maritime museum on the Icebreaker (a ship) that your kids would probably like as well.
You may also want to check out http://www.mackinacislandvacationrentals.com they have condos for rent which might be a great option with the kids because then you can do some cooking yourself, if you are so inclined. I have been thinking about doing this for our next trip.
You should definitely rent bikes (your kids would probably get a kick out of a tandem bike) and ride around the island. You can also either go horseback riding or rent a carriage that you drive yourself, which would probably be fun for the kids as well. I don't know if your kids are too old for this, but there is a butterfly house/conservatory on the island as well, I think.
I think for the kids first trip to Mackinac you definitely have to go to the Tea Room. There is also a great restaurant that is owned by the Grand Hotel called The Woods that is nice and has excellent food. The atmosphere is great too, it is in an old hunting lodge. It is a bit pricey though and you will want to make reservations. Your hotel can probably make reservations for you, that is what we do at the Island House.
Have Fun!
D.