Stick to Phuket, as said the transport is nerve racking and plenty of options to visit the outlying islands from Phuket, either north or south of the island.
Phi Phi is not what is was and Maya Bay is closed for a few years, think they just take you on a boat to the entrance now.
Patong is the worst place to stay on Phuket, north west is more upmarket and good for boats out to Phang Nga or Koh Yai Noi (bike nature tour). Going south Karon and Kata more family orientated but longer journey to get to the marinas/piers. Nai Harn has a nice beach and you can catch the boats from Chalong Pier.
Other sightseeing on Phuket - Elephant sanctuary (there are only 2 ethical ones), Phuket Town, Big Buddha, Wat Chalong.
Rain - had a fair few short heavy storms beginning of June but now back to lack of rain for a few weeks.