P.K.
I recommend staying on the island- it can be fun and busy during the day and becomes completely different and relaxing at night. In the past, I've found that the Murray Inn & the Inn on Mackinac both have had good prices, if you want to stay "in town". For something quiet (but also family friendly), check out the Inn at Stonecliffe. It feels very private and has beautiful views of the lake and bridge with a giant lawn for kids to play on (plenty of lawn games are provided). You can rent bikes right at the Inn and they have an outdoor pool as well. Don't miss the Woods restaurant (next to the Inn at Stonecliffe). It has a set-up-yourself bowling lane off of the lounge. No one seems to ever use it and kids adore it!