There are lots of opportunities for year-round outside activities here. There are several great hike and bike trails on the Greenway (free) and Ft. Clinch State Park (nominal fee) on the northern end of the island where you'll be staying. They're located across from one another on Atlantic Avenue - which is an extension of Centre Street in the Historic District. Ecomotion Tours also runs great Segway Tours in Ft. Clinch. Just go to their website to get the schedule. You didn't mention where you're staying but most of the bed and breakfasts offer complimentary use of bikes during your stay. Kayak Amelia does guided trips, but you can also just rent kayaks and canoes if you prefer to go it alone. They also have SUP tours (stand-up paddlesboards).

There are some less active outdoor pursuits that may interest you, as well. Amelia River Cruises goes out on a couple of trips a day offering a narrate history of Amelia Island and Cumberland Island; you can take a private carriage tour of the Historic District too. There are also trolley tours and a Saturday Farmers Market in town.

You didn't mention the dates in December that you'll be here but there are always things going on on the island. The best best is to go to www.ameliaisland.com to check the events calendar. Have a great time on the island.