Hello Sherry,
I've been to Playa del Carmen as a solo traveler for two 10-day stays over the last two years. I LOVE Playa and its people. Everyone I've met and interacted with have been unbelievably friendly and helpful. Even without speaking much Spanish, I've never had a problem and feel safe walking wherever I want to go. I'll be spending this November and December in Playa, and I can't wait.
Although some tourists are unsettled about the police presence on the beach and in the town, I feel safe with them. Unless you are partying hard or driving in an unsafe manner, they will not bother you at all.
I hope you will give the Riviera Maya a try. And remember, expect the best and you'll experience the best.