I dove the Destin East Jetty today; the water was very, very clear and warm (75 on the surface, 71 @ 50 feet). The incoming tide is the best, plan to end around high tide, since the current at the Destin Pass can really get ripping when the tide changes; the water gets very dingy and dark right after high tide, when the entire bay is draining out through the pass. You can park right on Gulf Shores Drive and walk into the beach right by the shower.
I personally believe that for the money ($8/car load/day), the St Andrews State Park Jetty is the best dive close to Destin...Pensacola is a very, very close second, but a longer drive for me. There is a really nice "kiddie pool" for non-SCUBA or snorkellers that has no current, unlimited visibility, lots of fish for the non-divers to look at, and really close picnic tables/pavilions. For divers, you go on the outside of the jetty and go as deep as around 60-70 feet, with great vis most of the time, fairly light current usually, and about a gazillion different types of fishes to look at. The one caution though is you MUST have a dive flag with you (they enforce this pretty regularly) and there is quite a bit of fishing line in the water, so have a knife, and keep a close watch out for your buddy...the only place I have been recently with more fishing line is Fort Pickens, State Park Jetty, in Pensacola (mentioned earlier by Hetland). Fort Pickens has similar admission, but it covers you for a week and I think it includes primitive camping. Fort Pickens has billions of fish, and there is some other underwater attractions to look at.
Good luck, have fun on the Gulf Coast!
Mike