June is actually one of my favorite months to go, as the crowds are down quite a bit but the NORMAL pattern in most of the country has maybe just 20-minute or so downpour late in the afternoon. It's more overcast and therefore cooler than the typical May, but the summer (March thru May) can get really nasty with the high 90s temperatures and high humidity.

Haze problems and climate change have been adding some unpredictability. Ko Samet is known for being one of the drier places year-round. I'd favor the gulf side over the Andaman side for beaches.