OK, there really isn’t any town/city of Punta Cana. Everything in the area is pretty new. Twenty years ago there wasn’t much there except sand and palm trees. Everything was pretty well built around tourism. The beach is exceptional.
Puerto Plata on the other hand has been there since Edison was an apprentice. It’s old, a little dirty, and there are motor scooters EVERYWHERE, including possibly the sidewalk. Traffic signals, when they were introduced, were treated as an indication that the power was on today. They’re a little better obeying them now, but it’s best to look in all directions before moving anywhere. Playa Dorada is a gated area and as such is pretty safe and nice to walk around. The sand is much darker than Punta Cana, but overall the beach is nice, but not spectacular. There are more and varied excursions to take and more to see. Towns and villages in the area are interesting to visit. Don’t miss the cable car up Mt. Isabelle de Torres (793 metres high). There’s a nice botanical garden at the summit. The view is spectacular. Just go there early in the morning as the mountain is generally clouded over in the afternoons. Ocean World is another not to be missed place. I have done business with a local tour operator (martin Espinal). His English is perfect and he had good equipment. If he’s still in business, I highly recommend him. If you go, drop me a line and I can give you contact information.