The "monsoon" here is year round. From May - October its the southwest monsoon, from November - April, the northeast monsoon. The word monsoon refers to wind. It is on average wetter and rougher on the Andaman coast during the southwest monsoon season, BUT what I have just quoted you saying is exactly the kind of "monsoon scare tactics" I hate to read. Most of the time the weather is good. Check my weather blog for the last 2 years.
I was there for 2 weeks form Feb to March, and we rented a car and drove form the gulf side to the Andaman sea, both coast has great diving. I have no regrets diving on either side. Saw allot of the country side that allot of people do not see. The drive was well worth it, garmin gps with the latest Thailand maps helped, :14:. It rain a bit, but it is the tropics, no big deal. So we found indoor thing to do, and Phuket has allot to offer when it rains. But it was not raining for days, 14 days in Thailand, only 2 rain days and couple of light passing sprinkles on another day.
Phuket is a very large island with plenty of jungle and even a national park. From your comments, it seems you restricted yourself to Patong. Since your wife likes Thailand so much, next time you come to Phuket, try to stay outside the tourist towns and you'll find the island to be quite idyllic, though perhaps not as unspoiled as parts of Tao.
Yes, Phuket had some nicer area, do get me wrong. We drove around the whole island. It was just not as relaxing as some other areas, I like the beaches up on the north end of Phuket better. There were beaches in Khao Lak that we did not sea anyone there for hours, and it was by our hotel. Phuket had alot to off, if you want to shop, you can go to Phuket town or the central festival mall. There is allot of night time actives over the more secluded area of Thailand. We enjoyed our time in Phuket. But for a short trip as the OP is planning, time is going to hamper his ability to see everything, and since he wants to get some dives in also, staying closer to the dive operators puts you closer to the touristy areas and still allow time to take in some of the local flavors. The beach side Thai Massages are always nice.
Think my next trip, I will try to see some of Northern Thailand, and see how much of Bangkok I can take, in a good way.