There are many paths into the park area, besides the main park entrances. These provide gorgeous hikes away from the tourist crowds. One might actually see the monkeys of the park instead of just hearing them. Inside, the paths will inevitably hit a park road, where one can hitch a ride on the park buses to other parts of the park.
Ask local motorcycle-taxis drivers to take you to the park but not the main gate, and they can show you a trailhead. As always, negotiate prices beforehand.