I live in Mexico and have visited Riviera Maya quite a few times.
In terms of hiring a car, you have 2 choices: go for one of the major firms like Budget or Avis and pay more, or go for a smaller firm like America Car Rental and pay a lot less, in the knowledge that they'll probably try to rip you off. I prefer the latter, but if it's your first time I'd go for a big company. Whichever you choose, make sure you buy excess insurance from another company before your trip (just google car hire excess insurance) as they are far more competitive than the extra insurances the rental companies try to force on you. Ignore any rental agent who says you need their extra cover, you don't. Also, make sure you choose the option to return the car with the same amount of fuel you picked it up with, or they'll charge you extra for filling it.
In terms of things to do, I tend to stick to the touristy stuff as that's really what the whole place is about: I can highly recommend seeing the light show at night in Chichen Itza: it gives the whole place an amazing ambience and you can see some beautiful stars too. Ignore all the tours the concierges / street vendors try to sell you: just browse google maps or trip advisor for things you'd like to do, and explore them yourself. There's a lot of beautiful beaches which are in general a lot quieter than the hotel ones.
You'll hear a lot of horror stories about it being dangerous, but it's safe providing you don't do anything stupid. Driving late at night can be risky: there's no street lights outside of the main towns, and you'll probably be the only car on the road, so if you hit one of the many stray dogs and damage the car, you could be waiting a long time at the side of the road, and will be a target for any dodgy people who happen to pass by.
Make sure you pay cash in petrol stations as they have been known to clone cards.
When driving, just follow the locals: make sure you're not the fastest car on the road, but equally don't religiously stick to the speed limit unless other people are: some of the limits are insane (stretches of 25MPH on a 4 lane highway for example) and if you actually do 25MPH you're at risk of being rear ended by someone flying past at 80 and not paying attention. Also watch out for the "topes" (speed bumps) which can be very high and will damage a car if you hit them too fast.
That's all I can think of for now: any more questions, fire away!
