When we went to Chichenitza they stopped by at local craft shops, but it was much cheaper to buy items on the actual site. Vendors set up and you can buy things and bargain. We got a little pather mask and a big carved item with the old Mayan calandar on it. Basically you'll see lots of masks, some carved wood plaques, some brightly colored china pieces, can't think of anything else right now.
I would recommend swiming with whale sharks if it is the right time of year. It was one of the most amazing experiences I've ever had.
As for eating find a place with tacos (real ones that are softer bread), so good and cheap! Otherwise I found alot of the food too overpriced and American.