X2 on Seafood Kitchen - food is better than Singleton's. Although if it's your first visit to the area, go to Singleton's for at least one meal. Daytime. You can see the river traffic, watch fishing boats, barges & the ferry. To find Singleton's take A1A out to the ferry. Singleton's is just before the ferry.
Mayport has 2 great parks. Pelican Roost right where the Navy ships go out in to the river to the open ocean. If you have a scanner you can listen to the basin info. The other is Osprey Cove located in the back of the base behind enlisted housing. Beautiful setting just not on the water. It is sure not as windy as being on the water.
If the New York is in port, get the # for their qtrdeck & call to check about a tour. We did that on our recent stay at Mayport. The hull has some steel from the Towers in it.
Day trip. Definitely St Augustine. Oh! Check at ITT for discount tkts for local attractions. We got discount tkts for the tram that goes around St A. You can get off & on as you want plus the drivers - most of them - are quite interesting with lots of knowledge. Plus parts of Old Town aren't easy to navigate or find parking.
Enjoy your visit!