I don't know of any gardens around the area, but WOW! I adore that part of the world. The Tulum ruins have a few areas of great plantings, but no real garden. (If I remember correctly, there were some GREAT agaves around the area.)
If you're renting a car, check out the Sian Ka'an Preserve. Beautiful flora and fauna in there. (Just be careful walking out nearer to the marsh areas, there are crocs in the area!)
I have a friend who stays in Akumal a couple weeks a year- I'll ask if she or her hubby knows of any!

Tulum is beautiful--we were there last summer during our cruise. There is a gorgeous beach right there at the Tulum ruins, and there are some beautiful plants growing all around the area, but nothing like a structured garden. We didn't explore any nearby places, so who knows what you'll find? Ask your tour guide or someone working there, and they could probably tell you. I've seen that there is a botanical garden near Puerto Morelos--check this link below.

Janey

Here is a link that might be useful: Puerto Morelos Mexico