Mayan Palace-Playa Del Carmen
You are going to my favorite place on the planet. Do your grocery shopping in Playa at either Walmart or the Mega Mart of Chedrui all good choices. If your renting a car all have parking lots. If not then take the bus from out on the highway in front of the resort for 1.50 per person and then take a cab back after you are done with your shopping for 18.00.
Read all the reviews in the review section on the Grand Mayan and Mayan Palace there is hundreds of dollars worth of information. With alot of dining recommendations. This area is so easy to get around.
The city of Playa is set up on a different type of grid the streets running north-south advance in 5's example 5th avenue, then 10, then 15.
The east to west streets run in 2's 2nd, 4th, 6th confusing at first, but once you get the hang of things just like being at home ha ha.
Playa is very safe, but also they are hawking timeshare everywhere you go until you just want to scream. Unless you are a profession tourist like I sometimes fancy myself and play the game and make some money and get some great gifts. Just remember its like drugs just SAY NO!!!
As far as food to bring along cereal, power bars, peanut butter, crackers. I would do most of my shopping once I got there. The store at the resort has many things and it would save you trip into town if your just too exhausted for laying by the fabulous pool. I also love the room service at the resort it is the same price as the restaurants and you don't have to wait in line or even get dressed.
When you go into Playa and walk down 5th ave. this street is closed to vehicle traffic. You can walk for approx. 20 blocks with places to shop and dine on both sides of the street. With more places one block to the east(ocean front) or to the west 10th. Have a great time.