The drive from CUN to Chichen Itza is straightforward and unfortunately monotonous. Once you get on to highway 180 you put the car in cruise and keep driving until you get to Chichen Itza. The tolls along the way are very expensive by Mexican standards. Most tolls in other parts of the country are around 30 to 50 Pesos but the Chichen Itza toll is a whopping 276 Pesos.
Right after you pay the toll though, there's a large hut where you can buy your entry tickets to Chichen Itza. This is an official booth so there's no haggling, and nothing untoward about the operation. It's actually quite convenient to stop there, get a bit of info and buy the tix. They even have a few pictures which they helpfully show you so you know to turn here or there when you get to Chichen Itza.
The speed limit on Highway 180 is 110 kph. It's unfortunately slow - were this road in Europe the limit would be 130 for example. You can cheat and drive at least 120 kph but there are police hiding occasionally so don't push your speed and your luck too much.
I drove from CUN to Chichen Itza then after seeing the site went on to Merida afterward. It was an easy drive and we made it without any difficulty. After a couple of days in Merida we drove straight back to CUN and again, made it without difficulty.