Camcolt,
I know it's easy for me to say because I've been there,but we felt very safe everywhere in Mazatlan. The taxi ride from old Down town to the La Playa was about 15 minutes. The Port is probably about 5 more minutes. The good thing about Hotel Playa is it is right in the middle of the Golden Zone.... All the shops. I think the taxi ride - which was actually a truck with benches in the back was about $5.00 per person.
Good luck with the decision.