What's the difference? In simple terms, think of Nuevo Vallarta as a suburb of Puerto Vallarta with the airport (PVR) in the middle. Kind of like how the Riviera Maya is a "suburb" of Cancun.
In fact, Nuevo Vallarta is the first in a line of "suburbs" of that makes up Mexico's new Riviera Nayarit. Also included in the Riviera Nayarit are the beach towns of Bucerias, Punta Mita, & Sayulita to name a few.
In Nuevo Vallarta, the hotels & resorts are mostly all-inclusive with multiple restaurants on site. Therefore, guests really have no need to leave the premises. In Puerto Vallarta, most of the hotels pre-date the all-inclusive wave. There is no doubt you're in a city and NOT the 'burbs. If you want a nice dinner, you shower up, put on a clean shirt, and find a nice restaurant every night. Puerto Vallarta has a variety of restaurants (some world-class) for a variety of tastes and budgets. Afterwards, Puerto Vallarta offers a bustling nightlife. There are a multitude of bars & clubs to choose from to party all night if you wish.
Nuevo, outside of your hotel's lounge, has no such offerings (at his time). Very little outside nightlife. Remember, you ARE in the suburbs. Of course, you can always easily venture into Puerto Vallarta from Nuevo by cab (about $17-$20 USD) and experience the best of both worlds.

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Where to rent/ Where to stay??!!! any help appreciated!
Hello! I am looking for some advice. I did some trolling around here but didn't exactly find what I was looking for.
We are planning a trip in March and are looking at Puerto Vallarta or Nuevo Vallarta. The family is somewhat mixed- some like culture and adventure, others just really want to lay on the beach with a drink. We do like to have fun and go out, but do not want to be part of a huge party/spring break scene.
Here is what we all want-
We want to rent a condo for all of us to stay at. We also want to be able to walk to restaurants/bars during the day and at night. We all are looking for a sense of a "community", meaning that we could walk up and down a beach and see things/visit places, etc. We visited Puerto Aventuras years ago and loved being able to walk around to places during the day without having to cab it, but then also enjoyed taking day trips to other areas.
Where would you recommend we look for a place to rent? Old Town? Nuevo Vallarta? Any suggestions would be so greatly appreciated!!!!
Where to rent
Without a doubt, you should stay in Puerto Vallarta. Nuevo Vallarta is not a "walkable" destination.
As far as condo rentals, we have no personal recommendations. However, be very careful in your internet search, as the area (unfortunately) is teeming with timeshare schemes. Your best best is to find a travel agent that specializes in family/group travel to Puerto Vallarta. Here's a site to get you started