I am planning a trip for this May in Mexico. My wife and I have a 2 year old. We are thinking a non-AI hotel is best for us because we don't drink alcohol, and enjoy good food. I have heard the food quality is lower at AI resorts.

Recommendations for where to book a hotel in Mexico, with good beach, walking distance to great restaurants, and with options for a day trip somewhere (see ruins or similar experience)?

Isla Mujeres.

My own experience of seeing ruins and eating well has been in the Yucatan, flying into Cancun, renting a car, and overnighting in a comfortable local posada in Valladolid to see Chichen Itza and Ek Balam, continuing on to Merida for Uxmal and RutaPuuc (if wanted), and passing through Coba on the way to ruins and blissful beach days in Tulum, enjoying the local cenotes and cuisine along the way.

But it seems you are looking for a gated resort property, but one without meals included?

Look into the Playa del Carmen area. There are many condos for rent and also smaller boutique hotels. MANY restaurants in Playa and day trip options as well.

If you are looking at the Yucatan, I would consider Playa del Carmen, Puerto Morelos, or Akumal. They all have calm water white sand beaches. Playa is the most urban, with wall to wall restaurants, shops and clubs one block in from the beach. Lots of nice condos and small hotels. Puerto Morelos still retains some of it's fishing village feel, and Akumal is a resort enclave of small hotels, condos and restaurants along two quiet bays with great snorkelling. The Akumal Caribe hotel might be a good fit.
Have you gone to the locogringo web site?

Puerto Vallarta (is my personal favorite and fits all of your requests).

Where are you flying into and will you have a rental car? With a two year old you will need to bring or rent a car seat and taxis do not provide them.
Since you mention ruins, are you considering the Riviera Maya area? Plenty of places to stay non-AI, including Hotel Akumal Caribe that zootsi mentioned, lots of condos on Half Moon Bay or in Playa del Carmen and some in Puerto Morelos.

Thanks for the replies. I did not think about the car seat yet. I was hoping we could take some kind of shuttle bus from the airport, but that might be a safety concern for the baby?

You should be able to find airport transportation that includes a car seat. But that is something you'd probably want to arrange in advance. In Mexico, it's common to see people just holding their kids on their laps in a bus or taxi. You may or may not feel comfortable about that.

You can arrange a private transfer from the airport, it has to be done in advance via email. I used USA Transfers last year as I was meeting my friend who had a car, they will provide a car seat for a small cost. Canada Transfers is another popular company, you can pre-order cold beers for $1 each.