Display navigation menu according to parent page

Hello all,
I was wondering if anyone know how a navigation menu can be assigned to a page based on it’s parent page.

To put that into context:
-Let’s say, Los Angeles and Santa Barbara are two parent pages
-From the back end, we created the menus that we want to use for each group of pages. (la-menu and sb-menu)
-Los Angeles Map, Los Angeles Restaurants are child pages of Los Angeles
-Santa Barbara Map and Santa Barbara Restaurants are child pages for Santa Barbara

In this case I would like Los Angeles, Los Angeles Map, and Los Angeles Restaurants to use the la-menu. Santa Barbara, Santa Barbara Map, and Santa Barbara Restaurants should display the sb-menu.

ULTIMATE GOAL: When creating a page from the back end, I would only need to select the parent page, and the menu will be displayed accordingly.

Is it possible to do this? What are the steps I have to take in order to do this?

Thank you guys in advance,
-Jenny