I am retired living on $40,000 annually in Palm Springs, California. 
What is the cost of living difference if I moved to Puerto Vallarta,
Mexico or Neuevo Vallarta, Mexico?

may I suggest Ecuador?
Ecuador uses US dollars as national currency and with 40k per year you
can live in a dream place, see http://www.vivecuador.com/ - you can
live a 4-5 stars life here for the expenses below: let me make some
calculations for you: you can choose highlands or peacefull beach
prices average:
Example:
- quito tennis club private exclusive condo: apartment: 
$350/month
- living expenses 3 people expenses - buying same or same quality USA
food, etc food..)
$250/ month 
- bills: water, cellphone, tal, light, etc: 
$120-150/ month
- for 800 month - 1.000 usd you can live  excellent life here same
costs or less for private beach apartment.

:-)
gmail: vimacompany