You can also look for it under the common name Yesterday, Today & Tomorrow. It grows really well in So FL. There's several growing near my house (zone 10). You should be able to find it in most of the local nurseries, probably even the big box stores like Home Depot will stock it down there.

Ardisia elliptica. Here is a link that might be useful: Florida Noxious Weed List

Even looks a bit like a Syzygium to me. The picture isn't clear.

Kristin, welcome to the forum. This is a GREAT place for a Florida gardener, whether just starting, or an old-timer with green thumbs, hands and shoulders. You will love it here. I started here over ten years ago and have learned just about everything I know from these forums. I had a variegated pittosporum and it grew like a monster. They have very few problems and are generally very healthy. I eventually pulled it out to plant some tropicals in its spot but if you just want a big ol' healthy plant, pittosporum will fill the bill. Carol