I'm still considering buying a house there. Depends on what you want to do. Generally speaking the North Side of the island is more active and has a huge public access beach on the east side (Main Beach) and the very fun old town of Fernandina Beach on the west side facing intercoastal. To the south you've got big condos, gated communities and the like. Jacksonville is an easy airport.
I think we just stayed at the Courtyard, which was an easy walk to the Main beach park. It's on the main east/west road (Jimmy Buffett highway) that runs straight to downtown Fernandina Beach. Takes all of 5 minutes. So I'd either get a spot near that Main Beach Park or walkable to downtown, depending on preferences. We also quite enjoyed the Mocama brewery (in a former car dealership), they have live music.
Mocama Brewing Company If you like nature, there are two islands south of Amelia that are state parks and are utterly unspoiled. Big Talbot and Little Talbot, wildly tropical. There's also Fort Clinch state park north of the island (north of town).