Peaks Island is the perfect day trip from Portland's Old Port. You can bring your car across, but it's not necessary. All you need is a bike, some water and a beach towel. Once you get off the ferry, you can explore the stores within walking distance. Once you are feeling like you want to see more, bike around the island. There are several places to store and admire the views. If you go from the ferry landing to the right, you'll come across a beach where you could park it for some r&r.
Just watch the weather! We've been out on a bike ride at the middle of island where all of a sudden it's pouring rain. Since the ride is short, we didn't mind. We raced back to ferry landing, bought new t-shirts and then found the nearest restaurants to watch the storm come in while enjoying some lunch.
Have fun on this quintessential Maine island trip!