We stayed at JAX NAS about 10 days in March 2013. It was a nice campground, no complaints. Easy access from 295.
To answer your questions:
1) What to do? - For a city the size of Jacksonville we didn't find a lot of tourist things. We asked various places and every time was told "There's not a lot to do in Jacksonville." and then they'd tell us about something along the coast to see and do. There is a greyhound racing track about 2 miles south of the main gate. It's not that far from the coast and plenty of things to see and do along the coast. Short drive to St Augustine and a bit farther on down to Daytona Beach. On base the golf course and club house is next to the campground and an easy walk. They have boat rentals. We didn't spend a lot of time on base using the facilities.
2) Base stickers? - Retirees do not need vehicle stickers. They do a 100% ID check and an ID card is all you need. Our vehicle sticker had just expired and I had planned on getting a replacement. Never had any problem getting on base at any hour with just our ID.
3) Sites, water, etc? - Some are pull thru and some back ins. We had a back in and no problem getting our 40 ft 5er in the spot with plenty of room for the truck. We had full hookup. They were going to do some upgrade/improvements on the lower sites in the wooded area. Don't know if that has been done. Those sites were closer to the water.
4) Boats, tackle, water temp? - We were told they rent boats. Don't know, didn't pursue it. Don't have any idea about water temp.
Make reservations. When we were there it was full almost every night. Reservations and registration is done at the Auto Hobby Shop. The people working there were very helpful and friendly. We called about 2 hours before arriving to confirm our reservation and they gave us our camp spot, told us to park it first and then come back. Good bunch working there.
We'll most likely go back this March.
Here's the website from Military Campgrounds with info, contact numbers, and reviews:
JAX NAS Campground