There are several options in Thailand, but in general first of all this here:
Diving in Thailand is - specially opposed to other locations in South East Asia such as Indonesia and the Philippines - not the best location to go to. Coral bleaching and overcrowding has severely deteriorated Thailand as a beach and dive location over the last 8 years, and even former AAA-spots as the Similan Islands but also Koh Thao in the Gulf have suffered a lot from rising water temperatures during individual record temperature summers. That said, it remains a matter of what one is used to in order to assess what is good or not. If you have been only diving in a muddy lake, Thailand is great. Once you have been in Indonesia, you will be surprised at the difference in reef health and how overcrowded Thailand actually is.
First of all, for the lazy, there is a aquarium diving in the center of Bangkok. It specializes on Shark diving. The advantage here is that you can see several types of sharks that you will never see otherwise in Thailand. On top of that, the Siam Paragon mall and the aquarium is something nice to see while in Bangkok. Ideal if you are on a weekend in Bangkok. Also you can go here around the year.
Since you will not find other dedicated shark diving in Thailand such as in South Africa or Australia (with cages, great whites and the like), any dive resort in Thailand can take you to locations that are most likely to be able to see sharks. The question is rather then for the best dive locations in this season in general.
The best location in Thailand is by far the Similan Islands, however between February and May. You can then also find Whale sharks there. But you have to go on a live-aboard since it is so remote. However, and since the west coast of Thailand is worst in the summer since the visibility is very poor, many liveaboards do not operate and some specially famous dive locations are even inaccessible. If you do not mind this and find an operator, you can have a quite private experience however. On the other hand, in locations like Phuket, Krabi and the places inbetween such as Koh Racha and and Koh Pipi are also not ideal - again the overcrowding and the poor visibility. Also, since they are so close to land, overfishing has impacted specially the shark population.
So the Gulf of Thailand is your best bet for this season, and there the more remote locations. Typical dive holiday locations in the Gulf Thailand are Koh Thao and Koh Samui, along with the smaller islands around the region. Due to its remoteness, Koh Thao is your best bet, most of the hotels there are dedicated dive resorts. While there was also a coral bleaching during 2010, it seems that bull sharks have returned since last year. Koh Pangan is a bit larger and can still reach Koh Thao dive sites by boat since the islands are only 35km away from each other, so you can stay in either of the resorts. I would make the decision dependent on the resort, it's costs and the flights that you can get which matter more at this point since this can have a major impact if you are bound to arrive and depart on specific dates. And if you care to not overspend or not to sleep in a shack.
So I would recommend to first look for hotels on both islands and see if those have an attached dive center. It will be easier for you than going to one hotel without a dive center and then having to commute to one every day. Transport is not ideal on these islands.