Of the three (and I have visited all of them), Acapulco is by far the most beautiful. Too bad about the current conditions, and I agree I would avoid it, although you would probably be fine. Acapulco is now mostly visited by Mexico City residents given its proximity. This makes it a more authentic destination than the other two (especially Cabo), where everything is geared towards satisfying the Yankee tourists. Also, Acapulco is an old tourist destination. Tourism from the U.S. peaked in the 50s and 60s. This gives it a very special feeling that I like. It's very pleasant in winter.

Cabo is the one that has developed most recently. It has the rugged beauty and dry climate of the Baja. However, the two towns are excessively touristy, and the stretch between them is an endless sequel of resorts. Not something I am attracted to. Once you leave town, most roads except main roads are unpaved. Safety-wise, it's between Acapulco and PV. Some episodes of violence have happened in the last two years.

Puerto Vallarta is by far the safest. It's one of the safest places I ever visited. The nice part is that the city itself is not entirely taken over by tourism. That is, it maintains a bit of Mexican culture. You have a choice to stay close to downtown or in one of the resorts along the coast. It is hot in the summer (but with great thunderstorms!). Best visited in winter.