A lot of people own homes and condos there with the exception of the Omni hotel so you can expect quietness and just pure relaxation.
There are boutique shops, tennis courts (where women's tournament used to take place), 2 golf courses with some of the hole right by the beach, an expanded full fitness center (where they film and host the biggest loser), lots of parks with Wifi, swings, Segway rentals, walking trails by the marsh and a couple of restaurants.
Marche restaurant which where everyone gets lunch or coffee or ice cream. Service is not great, pricing is not amazing either but when in Amelia. The other option is to come with your grocery all planned out (shopping centers are just 15 minutes away) and just enjoy the beach if you were lucky to rent a beach front condo otherwise, pricing for the Omni restaurants are pretty pricey with a very basic selection.
The Omni hotel has a beautiful setup, beach front as well as a completely renovated pool area with fire pits everywhere.
We stayed with our in laws on a beach front condo so 80% of our meals were cooked which I would recommend.