I was in Playa Del Carmen in February and it was very safe. There are always lots of people on the streets, and also a heavy police presence.
I've also been to Mexico City a lot and in the center of the city have never felt unsafe.
But if you really want to feel safe go to Merida. It's considered to be the safest city in Mexico. And it feels it. And it's a very beautiful and clean city. It's very calm. Great restaurants. But March through August it is very hot. So be prepared if you go during those months. I was there twice this year and am exploring living there.
And if you need the beach it's about 20 miles to the Gulf of Mexico.