We go to P.V. a lot. Los Muertos Beach is very close to the Zona Romantica. Take one of the yellow cabs to the Cuale. This will allow you to see much of the town, stroll through the Cuale in the Zona Romantica and have a great day of beach activities at Los Muertos Beach. (Only two blocks away toward the coast.) Have a margarita for me at Burro's Bar on the beach right there. River Cafe and Le Bistro are both great choices for a fabulous lunch and both restaurants have a great view of the river there.
My favorite beaches in P.V are Yelapa, Sayulita, and Piedra Blanca, but these are a bit of a jaunt by taxi or water taxi. The Krystal Hotel is a fine option but you will experience very little Mexican culture.
In Mazatlan, the best beach is Stone Island. As you leave the cruise ship terminal turn left and walk about 1/3 of a mile. Go down the dirt road and take a water taxi ($2.00 per person round trip) to stone island. The beach is quiet and a lovely place3 for a nice long walk. "Carmelita's" is a very good outdoor restaurant there on the beach. This beach is almost too quiet in the morning. You might want to hop a taxi to the golden Zone in the morning for shopping. Then go to Stone island for a nice lunch and an afternoon od beach fun.
Mazatlan and P.V. are far more safe than most U.S. cities in my opinion.