Surat Thani sits on the Gulf of Thailand coast and has a wetter, longer rainy season than the Andaman coast resorts. The wettest months are October through December, when the northeast monsoon brings heavy rain to the Gulf coast — this is the same season that Koh Samui sees its worst weather. January to August is generally drier, with the most reliable weather from February to April.
The city itself is worth visiting at any time of year since sightseeing is minimal, but if you're connecting to the islands, check the ferry schedules during bad weather periods — services can be disrupted in rough seas.