There is always somewhere good to dive at any time of the year in SE Asia. It is the coral triangle after all, so the richest marine life on earth.
First off I would say Thailand is a good place to start. But if diving is your priority then you would be better off going south to Malaysia and Indonesia than you would to Cambodia and Vietnam. Those 2 countries are places where yeah you can dive if you are there. But Malaysia and Indonesia have some of the most interesting and exciting diving on earth. Proper dive destinations.
June to August is low season for the Andaman Sea so Thailand's Similan islands are out. You could do some dives from Koh Samui or Koh Tao to settle in. Then get yourself down to somewhere awesome like Sipadan in Malaysia or Bali, North Sulawesi, Komodo or Raja Ampat in Indonesia. That's some real diving: tonnes of fish, manta rays, sharks, mola mola, big stuff, small stuff colourful reefs etc. Or just give Thailand the body swerve and concentrate on Malaysia and Indonesia (you can fly Kota Kinabalu to Bali direct now).
Hope that helps. Let me know if you need more.