Pat,
I'll chime in here just for info but following any of the suggestions listed so far is good.....
I must come to the defense of diving in the Gulf off the Clearwater, Tampa, St Pete area. In the over 200 local dives I've done offshore right here I must say that it is some of the best (and most volatile) diving I've done anywhere in the world! Divers just don't give it a chance and some don't like the boat rides off shore, etc. To be sure it is definitely not a "canned" dive destination - it is offshore and an adventure but you will see creatures you aren't likely to see anywhere else. And viz ranges from 5 ft to 120 ft. As said the diving is very volatile but the abundance of fish life can be amazing (fish like bad viz BTW......
). Our goliath grouper here is the gulf are traditionally larger than the ones off the Fla's East Coast and we have more abundance of them. But the goliath grouper populations are recovering all over the state and even up into southern Georgia so there is a good chance you will be able to experience these fish. And they are an experience as there is nothing like seeing a 7 ft goliath grouper and then having it "boom" near you!!!!!! Japanese kodo drums then are pale in comparison I think! 
Plus I've seen mucho bull sharks offshore here but seeing them in an non-baited/non-spearing - natural environment is challenging for photography though.
But as Jeff says Jupiter is a good bet if you want to drive to the East Coast. I like Jupiter a lot more than points south. In Sept the goliath grouper may still be aggregating there - I've seen them aggregate between August and way into October some years. Jupiter Dive Center has a great captain, Mike -- but personally I'd go out with Randy Jordan who now runs Emerald Dive Charters because he founded Jupiter Dive Center originally anyway and knows more about the diving in the area than most everyone - you can book with him through Scuba Works new location on Hwy 1 in Tequesta-Jupiter area.
http://www.scuba-works.com/
The Hole in the Wall (SE of Jupiter, FL) dive is really cool too and I think I've done that dive almost 30 times now. We have seen everything from sailfish on safety stop there to last time when I dove it - 30 mahi mahi including the bull. On the macro side I've seen the small african pompano (threadfish) there and interesting small and colorful deeper reef dwellers but the sharks and huge goliath grouper, etc., are the stars of that site I think. Just be prepared, that dive can be deep as it is easy to hit 140 ft and the currents can kick up and be tricky - a few divers have lost their life there.
Plus Blue Heron Bridge, Riveria Beach (W Palm Area) is fantastic for "Florida Muck Diving" but be sure to learn the currents there as you sure don't want to be caught under one of those bridges during a full or new moon tide shift!! There is lots of info about how to dive that place on the web if you want to go.
Sharks' teeth in Venice are great as David says!!! Of course you can just do the Venice shore dives for them also but David's suggestion will give more yield for first time probably! Searobins and lined seahorses are commonly found there if one isn't all wound up in stirring up the sand and silt looking for teeth!
There is also another local shore diving spot on the West Coast Florida fairly near Venice that is the Boca Grande - Old Phosphate dock. Personally that is one of the best dives around anywhere if you hit it right. We saw over 80 goliath grouper there several times, dozens of nurse sharks and southern stingrays, 100+ tarpon, scads of jacks etc but be warned there are bull sharks there too and it is shallow - not somewhere I'd like to have to swim back on the surface in low viz for sure.......
Plus one other shore diving spot nearer Tampa off Bradenton called Spanish Rocks where I've seen seahorses, 100s of searobins, weird stuff - plus bigger stuff like tarpon too.
Thing to remember with West Coast Florida shark tooth and shore dives you need to do them in very calm periods with no wind or better yet East Wind. If you do the Venice shark tooth dive with Westerly winds blowing and/or recent thundershowers you will get zero viz for sure!
So Pat, just to confuse you - oh not really as I mean well -
. It just shows that all these spots are within a 4 hour drive of Tampa Florida and they are all definitely worth doing and most are a pretty unique experience. As far as photography, well they are more volatile but if you do get something it is likely to be something others don't photograph a lot - especially off the Gulf Coast here.
Of course you could also just take a relaxing drift dive on the freshwater Rainbow River which is 2 hours from Tampa and very worth doing (one of my favs) - just try to do it during the week so the traditional 100 to 200 foot spring run viz doesn't get mucked up by lots of student divers. Several operations can drop you up river for a drift back down but you could check with Bird's Underwater first:
http://www.birdsunderwater.com
of course Sept is usually too early for manatee but you could also get an update from them.
My advice - make the effort to dive within a 4 hour shot of the Tampa area - West or East Coast and you will have an adventure for sure (and maybe even come out of it with a couple of pics????)
Of course you can always go down to the keys but you really don't have to for some area-unique diving!
Best, Carol