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I've been to the RIU Palace Riviera Maya four times over the last 10 years, for at least 10 days each time. Never had any gecko sightings in the rooms, or in the hallways, for that matter. You can always book your room on the third floor, close to the main (lobby/admin) bldg. I don't know if you have a general creature thing going on, or just geckos. There is a pair of tapir-like creatures (I forget what they are called in Mexico) about the size of large cats that live in the bushes in the center garden and fountain area, but they are rare to see and shyer than geckos. No iguanas on the property, either (just lounge lizards by the bars). You're more likely to find iguanas by the beach at the hotels in the Zona Hotelera of Cancun on Av. Kukulkan (such as the Oasis, for example), on the Caribbean side of the strip. I found geckos outside on the third floor windows at night in Kapa'a (on Kauai), and they're not afraid of haole tourists. The most exotic creature I had to deal with was a lost bat in the buffet dining room one night about 10 years ago in Playa del Carmen, and the nicest was a morpho butterfly that was going to get chopped up in the ceiling fans that I finally caught gently in flight and took outside to release. Got some applause from the dining room, too. Don't let geckophobia keep you from the most beautiful place on Earth. And don't cheat yourself by settling for Cancun (where the chances of catching crabs is always good, and great at Spring Break). If you go, say hi to the main lobby bartender, Islas, and make friends with him. He himself is a show every evening after dinner (in the event that the nightly floor show isn't to your liking), and if you hang out until closing, he might let you tag along to the hottest party spots in PDC.