June is far from the best time to go to Koh Chang, Years ago when I used to frequent the island on a regular basis, virtually all the dive shops closed between May and September due to large rainfalls, rough seas and consequent low customer demand. Koh Chang is one of the wettest places in Thailand, see the att'd average rainfall (
http://iamkohchang.com/koh-chang-weather) with average rainfall of 902mm for the month of June, not only considering diving, it can simply be unpleasant and difficult to be on the island at this time.
I believe now some shops operate on the island year round, as anything reliant on the weather it's just your luck on the day, even during the rainy season the weather is obviously not always bad, but with such a short time spell as you are looking at you could quite easily travel to Koh Chang and find yourself unable to dive.
Also Koh Chang is not the most easily accessible place from Bangkok you are looking at around a minimum 4-5 hour road trip + ferry crossing and onward travel on the island to your chosen resort, so you need to allow 1 day each way for your travelling to and from the island.
Personally I would stick to the Andaman sea, also Koh Tao, although far from my favourite location in Thailand may be worth consideration.
