We walk everywhere. It's part of our trip, we really like to to a little walking tour every morning after breakfast. Our walks tend to end at Schooner Wharf at a little before noon so we can enjoy the end of morning happy hour, and then listen to Michael Mcloud at noon.
Bike rental is a good way to travel to any of the beaches on island, or maybe to stock island for lunch (Hogfish Grill) You can rent bikes at Pilot House. Virginia, and Daniel are very helpful with that sort of thing. Be sure to ask them for advice on restaurants, and bars. They are both locals, and love to help guide you to good spots for whatever you are seeking. As for scooters, I am sure they could help you with that as well.
It is a small island and we like moving a little slower so we can take it all in. I'm on an island, it's hot, I try to adjust to "island time". The walking also helps burn a few of the those extra calories from the great food, and drink.
You are going to love it!