The Tulum ruins are best very early in the day. Leave mid-day for the caves ( but you need to protect your equipment from the water). The mangroves are great towards sunset. The beach in town is the best. However the beach below the ruins offers great rockscapes.
Not directly photography related, but the beach just below the Tulum ruins is probably the most spectacular place to go for a swim in that area. So don't forget your trunks when going there. Seems a bit odd to enter the historic site with a towel and a snorkel, but you're allowed to do so!
As for interesting (photography-wise) places related to Mayan culture nearby Tulum, check out Coba (closest), Chichen Itza (spectacular, but usually quite crowded) and my favourite are for architectural highlights, the Puuc region with the sites Kabah, Sayil, Labna and Uxmal (splendid architecture, but just as big and crowded as Chichen Itza).
For the more adventurous and if you're willing to travel a bit I would also recommend Calakmul, one of the largest and most important of all lowland Maya sites in the most southern part of Yucatan, some 35 km from the Guatemalan border. Very remote, almost 50 miles from the nearest village with a core area covering nearly 2 square kilometres. The site is rarely visited by tourists and located right in the middle of a biosphere reservate. Wonderful opportunities to encounter rare animals like jaguars (Balam), if you're patient.
Structure II in Calakmul, an immensely large pyramid, rests on a huge platform (ca. 125 by 140 metres) and with it's height of almost 40 metres you'll have an excellent view across the dense green jungle below, stretching to the horizon on all four sides. Spectacular sunrises and sunsets.
I couldn't resist mentioning this pyramid as I proposed to my wife on top this place a few years ago - and we're still happily married...