Many choices in this area (also see FSKA's (Jax) website - http://www.clubkayak.com/fska).
One of my favorites is around Little Talbot, it's short (13 miles), and, depending on conditions, allows a choice of 'return' - via ocean (around L Talbot) or inside creek (around 'Long I'). (depending on your skills, if the swell is 1-2', it's safe on the outside - the most 'difficult' part is going out from Nassau Sound & coming back in at Fort George inlet (against a moderate tide)).
1) go 'clockwise' around Little Talbot I:
2) start from from under A1A bridge (Alamacani) or from Huguenot Park (nominal fee to get in, $1 if before 10am).
3) ***** START ABOUT 1 HOUR BEFORE HIGH [Simpson Creek station] - in order to be at the 'height of land' on Myrtle near high tide (if you 'miss' it, you will 'sit' for a couple hours).
4) return via Simpson Creek or the ocean.
(for a 'route' map showing the 'ocean' choice - see http://tinyurl.com/7btpt72, then click on the arrow to the right of 'Myrtl_13' (Simpson Creek is to the west of Myrtle)