Hi Angela,
Congrats on making the big move to our "Happy Island". I have a toddler daughter and a pre-school son so i know how important it is for them to socialize.
Now we tend to do things the island way so we dont have an " organized" mommy group. Play dates normally happen when kids go to daycare the mommies meet up and arrange other events with each other. Most times its beach barbecues, birthday parties and so forth.
You can also do baby yoga at Praña, ( a pre and post natal yoga center) There are also options for baby swimming classes ( we start them early here).the butterfly farm is a toddler favorite as well as our animal garden.
There is also a baby play zone at Palm Beach Plaza so he can run around and meet friends. (And burn off energy yayy for that!!)
I'm pretty sure there are more things but they just haven't popped in my head yet.
I'll let you know when they do.
Good luck,
Sasha