Valencia neighborhoods

Hola,

We are Expats presently living in Colombia for over a year. Prior to that we lived in Panama for 3.5 years and are from Long Beach, California, and Oregon.
We are looking for suggestions on neighborhoods to live in Valencia for our next adventure.
Close to metro, beaches, International airport, and quiet areas. Any suggestions or advice is appreciated. We will be visiting in April and May. Also, we have our retirement Visa's here in Colombia. Do we start our Visa process here or in Spain?
Gracias!
John y Susan

Regarding neighbourhoods I love 'Botanic'. 'Abastos' and 'Pexina' seem well connected, quiet, with many local shops and supermarkets.

Muchas Gracias!