It has been a good choice for us to start in Phuket. Initially we thought that it will be a vacation rather than full blown parental leave (whatever that means). Basically we planed not to care about anything and just enjoy the time (I hope we will continue doing that in other countries as well).
Phuket was fun - a lot of tasty food (too bad it is hard to be hungry when it is hot outside), very nice sandy beaches (some are more sandy than the others), sunshine (almost) every day.
Asia is great when it comes to food and there is so many local markets where you want to try everything (preferably multiple times) but I think Alena would not approve of me being 100kg dude. But it is relatively easy to find good, tasty cheap food when you go to those markets.
I am not much of a beach goer myself, I prefer shadow and a cafe rather than beach, sand in your swimsuit and itchy skin from the sea-salt. But Phuket was very good when it comes to beaches. We have been to two places next to the sea (Patong, Nai Yang) and both have good seashore. Patong had a lot more people there and a lot more movement so if you plan to party and have fun then it's your destination. I went for a run at 5 am once and many bars were still open from the day before. Nai Yang is more a family place and a quite one. There is not much to do, but to swim and walk around. I like the beach there because it has treeline which provides shade. The beach is very baby-friendly with smooth slope into the water. The sand is a bit too grainy so you have to carry a lot of it in your swimsuit. Next to Nai Yang is Mai Khao beach, next to the airport where you can planespot and the beach itself is also very good, not many people there (except the airport spot).
Bottom line if you plan Phuket visit and you have a baby go to the Nai Yang (not for too long though because you will get bored).
Tomorrow we are leaving Thailand and head to Malaysia (Penang).