I feel very safe in Playa Del Carmen, it's a very welcoming area. Don't just assume because you've heard stories and found it on a list that you're going to get mugged while there.
For fishing you have a couple options, go with a deep sea charter (closest option) or you can go north to Isla Blanca or south to Ascension bay for bonefish, snook, permit, snapper, cuda, and tarpon.