If you care about pizza then you should head over to Rafaello's off the corner of 60 x 51 sometimes surly service which you can just overlook because the pizza is real southern Italian made in a wood burning oven by a real southern Italian...they deliver too if you just can take abusive service.
If you care less about pizza then you should try the new Oliva on the corner of 56 x 49. Everyone raving about the home made pasta from a Roman chef. Informal small dining room and take out dishes for groups of 4 or 6 are a great option for eating at home.
If you need pizza and pasta you can try the newest location of La Tratto on the corner of calle 55 x 60. Here the service is friendly and you can dine under the stars and giant trees in Santa Lucia park. Go on Thursday if you want to see the Serenata Yucateca. It's basically south beach Miami atmosphere with american style food for the richie rich locals. Happy Hour at the bar is the place to get your feet wet.
If your thinking of buying or renting a house then you should try Rescoldos a "Mediterranean Bistro"
on Calle 62 x 41 & 43. The owners are Greek/Canadian and it's a popular hangout for the expat community. The food is heavier here than with the Italians at Rafaello or Oliva but more home made than the factory line food served at La Tratto.
Some people have enjoyed their pasta at Trattoria La Pasta but I've not had the pleasure. It's on Paseo Montejo x 39 & 41. I just never eat Pasta in restaurants unless I'm given no choice...
Now if you only care about eating Italian food and you want to do the Yucatecan tour of Italian restaurants owned by Italian I will give you the list of the most popular places where you have the best chances of authentic cuisine...
Osteria Picolli is the newest and maybe the best place to start on the Prolongacion Montejo.
Villa Italia is well established and has it's loyal followers on the weekends it may be hard to book.
Piola is far out near City Center
Vite Da Bruno in the nearby suburb of colonia Mexico