Dude.... About a month ago, I was more or less exactly where you're going. Well, we went to Cozumel, which is the island just off of Playa Del Carmen, but we did spend a lot of time in the Playa, and in Mexico.
First of all, Yes, you can climb the temple at Chicen Itza (we went there, there are some places that are roped off, but the majority are free game... You can even climb around the Ball courts. It's really cool). If you go to Chichen Itza, make sure you have a tour guide, those guys are amazing, and the background knowledge makes seeing the place that much more interesting.
There are some areas of mexico that are pretty... Squallid... But the Playa area is a completely safe tourist trap. Awesome street performers, cool stores, there's even a starbucks somewhere near Cozumel (walking distance).
If you can, I'd say to go to Cozumel (Stay in the Hotel Cozumel, it's a fantastic place with a private beach, scuba lessons, a nice pool if you want to stay in, and a great bar) The LCDH (which is part of a HUGE strip of stores that your wife will spend days at) is walking distance from the Hotel Cozumel. If you don't stay on the Island, then you'll have to take a Ferry to playa, and the LCDH is directly across from where the ferry docks, it'll be the first thing you see.
Do some research and make sure you know where you're staying, but the vast majority of that area is perfectly safe (as long as you don't spend too much. It can be dangerous for those lacking willpower; like myself) But if you stay in the area of Cozumel, Play del Carmen, LCDH, etc, you will never lack for things to do, and you will be nice and safe.
MAKE SURE YOU LOOK UP HOW TO SPOT FAKE CUBANS. Just do it again to be sure.
And don't buy anything that isn't from LCDH. Even if you can spot a fake... Just don't risk it.
Those were from personal experience and may not apply to you.
