Camping is popular in Puerto Vallarta. There are several stores downtown that sell everything that you would need for camping. There are lots of tour companies in Puerto Vallarta that offer camping, hiking, and other outdoor adventures like zip lining and rock climbing.
I used to work at a hotel for 4 years as a concierge and used to send people every day to all kinds of tours. There is a popular one called Outdoor Adventurer, which is a tour that includes tours going to the mountains, zip lining, waterfalls, camping, hiking, and jungle trekking. They also have ATV tours where you’ll go all the way up to the mountains, cross the rivers and see some animals in the wild while you’re on the ATV. There are about three canopies here, one of which has the longest line in Latin America, about 700 meters (2,300 feet). It is above the river so the view from there is amazing. There are islands around Puerto Vallarta and there is a lot of snorkeling and whale watching tours too. There are a lot of outdoor activities that you can do in Puerto Vallarta.
(Rappelling into a river near Puerto Vallarta, Mexico, pictured.)