does brink only take place in container city and the shipyard....., or does it take place in the entire island of the ark?

nah there's 8 campaign maps and 2 bonus maps
edit: these maps are also spread out over multiple areas of the island

As far as I've seen, some of the other maps are: The Prison and the Airport.

The Airport
The Prison (?)
The Aquarium
The Container City
The Reactor ("what if" mission for Resistance)
The Shipyard

I can recall these from the top of my head.

Alright cool, THANX....i was afraid it was only going to take place in those 2 cities...and when i saw the actual island on the website i was suprised

The map where A Matter Of Class took place is called Security Tower, if that's what you meant by Prison.