My wife and I spent three weeks there last November/December. From the research I did, September is better in the Gulf of Thailand (Koh Samui, Koh Tao etc), and although the diving is good, it is not as acclaimed as the Andaman.
Couple of suggestions here. The best website I found for information on Thailand was
http://www.travelforum.org/thailand. You'll get responses from people who are there right now. Also, Mark, who runs the forum, lives in Phuket and has travelled extensively throughout Thailand. I found his recomendations to be excellent. I was a little cautious at first (because he is in the travel business) but we didn't book anything in advance and when we shopped around in Thailand, his advice was right on the money.
He is going to recommend a stay on Phi Phi Island at Phi Phi Island Village. It is one of the nicest beaches I have ever been to, and there is a gold palm PADI shop on premise. It is about 25% more expensive than the shops in Ton Sai bay, but the boats and service are much nicer. Phi Phi is really the diving capital of that area, and I would recommend at least a few days there. That being said, there are multiple diving shops in both Phuket and Phi Phi, and booking in advance in Thailand is somewhat dangerous, (and, foreign to Thais). I HIGHLY recommend getting there before choosing a dive shop, and definately don't slap down any money in advance as the Thai culture is built around haggling. Pretty much everybody who dives that area will tell you the same thing, unless they have a friend in the business there.
Check out a book by Paul Lee, The Dive Sites of Thailand. I got it on Amazon, but it is available all over Thailand (even in Bangkok Airport).
There is a standard 3 dive day trip that all the shops do for 3200 baht (fixed price at all shops, about $70US at 45 bht/$) The three sites are halfway between Phi Phi and Phuket and it is also a highly recommended day trip: Shark Reef, Anemome Reef and the King Cruiser Wreck (the wreck dive is not described in the book as it was published before the ship went down).
Thais are great people and Thailand is a beautiful place, cheap if you do it right. We did a 5 night 4 day liveaboard with AOW cert for $425 US. Great diving (Similan, Surin... make sure you get a dive or two at Richeleau Rock if you go that route). We also did about a dozen dives in and around Phi Phi, but didn't get down to Hing Maueng/Daeung, they are two of the best sites in Thai waters, but about an hour by speedboat from Phuket/Phi Phi so trips don't leave daily and they are generally put together last minute the night before... just walk down the street in Ton Sai bay, there are literally dozens of dive shops (more than bars, and it is a party island too). I really really regret not getting down to those sites. You might find a liveaboard that does a two or three day trip there and the '5 Islands', which is also supposed to be spectacular.
Don't hold your breath on seeing a whale shark. I just did a liveaboard with a gentleman who has been diving Thailand at least one week a year for 10 years (his buddy owns Moskito dive on Phi Phi, one of the most reputable dive shops in the area, the other I would recommend is White and Blue, both have websites). Anyway, he just saw his first whale shark ever last week in the Galapagos. Although they are there, and people saw them while we were there, many of the local dive bums had been diving the area for months and not seen one.
That being said, the diving was awesome, landscape beautiful and prices quite reasonable. I, personally, really liked the food. Do check out travelforum.org, and also phuket.com (comercial, use it as a guage, but many of the businesses that sound huge and well established are tiny little one man operations with a nice website but not much else). Use the information as a barometer. Travelforum, on the other hand, is one of the best travel websites (message boards) I have found anywhere. You'll get good advice, quickly. If someone posts bad advice, a half-dozen people will quickly dispute it. Unfortunately, there isn't a huge amount of diving information on the site, but you will get some feed back. It is also easy to tell who is giving the advice (if the English is perfect you'll be able to figure out if it is Ozzies, Brits or Americans, if it isn't so good with phonetical spelling errors, somewhere in Europe, if it is horrible, it is coming from a Thai).
Have fun, it is a very laid back place where you can litterally book just about anything right on the spot. For instance, when were in Chiang Mai and realized Mark's suggestions were on the money, we went into a local travel agent and booked two nights at Phi Phi Island Village the morning we flew to Phuket. We couldn't get to Phi Phi that day because there were no more ferry's. When we got a place to stay in Phuket (Kata Beach, little tiny bungalow on the beach), I sent an email at 9pm to the booking agent and they picked us up and drove us to the ferry at 6am the following day. I could tell you a dozen similar stories from the three weeks we were there.
As usual, I've rambled...