I live in Puerto Plata since 2004 so I guess I can help with this one ( haven`t been to the other 2 destinations you mention ) Punta Cana is fine, but most travelers you`ll find there are baby boomers, people in their 60`s and fun is limited to the resorts, nothing outside the walls.
In the North coast there`s Cabarete, Sosua and Cofresi and that means you get a lot of young people and sports lovers ( Cabarete is the mecca for kite surfing worldwide ). The place is a long stretch of beach lined up with clubs, restaurants and surfing schools, plenty of beautiful babes from all over the world.
Sosua is a bit more laid back but has an active nightlife, excellent beaches and many restaurants. The bay is really nice, I`m adding a photo here and I hope here don`t mind, I know the owner of that hotel shown there.
Fishing in Sosua is pretty good, also snorkeling, diving and lots of other activities. Recently the new major in town set new rules because the chicas and vendors were told to stay behind doors, meaning that a single guy would have to visit a bar in order to see easy women, as opposed to having them on the streets hanging around as they used to.
Other areas of the North coast of the DR are Cofresi, which is for romantic couples and older people ( no chicas or loud music there ). There is a lot to enjoy and contrary to other destinations within the DR, you get forest, mountain and beaches all in one package.