Just my opinion on the Pacific side ...
Safety: If you aren't in a cartel, or aren't buying/selling drugs, then you're pretty safe. Crime happens everywhere, so nothing is 100%, but the cartels account for the majority of crime and they aren't targeting tourists down for a week or two. Pickpockets and unscrupulous taxi drivers - well, yes - they do target tourists ... but I personally don't know anyone who has been pickpocketed, and if you always get the price of a taxi up front you'll avoid getting ripped off.
Best time to go? I preferred the Summer months as there weren't that many tourists from the USA and Canada. The last thing I want to do is travel someplace to wind up being where I came from. The issue with Summer is that any of the Méxican coastal towns are going to be HOT and HUMID. It's also rainy season and there can be some real doozies, but rain usually comes at night. If you go out in the mornings, stay in during noon and afternoon, then go back out in the evening things are much more enjoyable! And always carry a bottle of water, and walk on the shady side of the street!
Towns: Cabo San Lucas is more of a party town than the other cities. It is the place to go, however, if you want fishing and golfing. Mazatlán is a city with a little tourist area. Puerto Vallarta is a tourist area with a little city. Acapulco is stunning. It's like Puerto Vallarta all grown up. Haven't yet been to Manzanillo or Puerto Escondido but they're on my list.
If you want a town with the flavor of México then either Mazatlán or Acapulco would fit. Mazatlán is semi-tropical and the beaches are some of the best I've ever seen. Stone Island wins the beach award for me. Cabo and Puerto Vallarta are geared towards tourism. It's still México, they just don't have the same feel. Cabo is desert and the beaches are often rocky. Puerto Vallarta is tropical, and the mountains come right down to the ocean. Of all the places, I think it's the prettiest. Acapulco also has mountains down to the ocean, but has been developed so isn't jungle like Puerto Vallarta. It's true that crime is higher there - but if you aren't wandering back neighborhoods at night you should be good to go. Since tourism from outside México is way down in Acapulco (plenty of Méxican nationals still vacation here), you'll see a more authentic Méxican town than in previous years. If you go to Acapulco make sure to find your way to both Barra de Coyuca and Palao.
For a first time visit I would recommend a Méxican Riviera cruise. You'll see Cabo, Mazaltán, and Puerto Vallarta. If you just want one city, I would recommend Puerto Vallarta. The city is beautiful and there's a lot to see and do. Most people speak English there so you'll be able to communicate without having to get google translate involved

There are also a ton of hotels, both in Puerto Vallarta proper, and North in Nuevo Vallarta. I won't speak to an individual hotel or chain as I don't know your budget and what level you find comfortable. Search the booking sites or ask specific questions here. Once you've gotten the feel of Puerto Vallarta I'd branch out to the other vacation spots. Acapulco has different areas - the Diamante area is similar to Nuevo Vallarta in that it's a ways away from the main tourist area and more upscale (re: pricy). Mazatlan has two hotels, the RIU and the Pueblo Bonito Emerald Bay, that are a ways North of the city proper. I feel places like these are where you go when you want some sun and relaxation and don't want to go off property much. You could be anywhere in the world though - if it weren't that the staff were mainly Méxican you'd never know you were here.
EDIT: Try NOT to do an all inclusive. Food, pretty much anywhere in México, is excellent and inexpensive.
I did the cruise in 2010, bought a timeshare in Mazatlán in 2010 (fixed Summer week), then bought a floating week in Puerto Vallarta in 2012. I bought an apartment in Mazatlán in 2016, and moved here permanently a little over a year ago. Fun fact, you can often trade one week of a USA/Canada timeshare for two weeks of vacation here in México. Just keep an eye out for specials and grab them when the appear!