If you want integrated you're best off going traditional for the distribution. That means in-wall and/or in-ceiling speakers from the brand of your choice, being driven by a multi-channel/multi-zone amplifier and controlled by a multi-zone controller/pre-amp. Also available in integrated solutions. Monoprice has perfectly serviceable in-wall and ceiling speakers at good prices.

You can locate the amplifier(s) and other equipment wherever you'd like, together, and then tie your sources to them - which can include multiple of the same type of product if desired.

Brands for whole-home distribution: URC, Russound, Niles, Xantech and others.

The benefits with this approach: Stealth installation with minimal or no equipment visible in any given listening room. Centralized equipment location and the ability to control individual zones from that central location or any other zone.

An alternative is the de-centralized approach where you can still use in-wall or in-ceiling speakers, but with source components and amplification in each zone. Here you can connect different Sonos or other similar devices in each zone. Sonos has the benefit of offering amplified models. You will be able to control the zones from anywhere in the home using a wireless network if you go Sonos or Squeezebox. To do centralized control/automation you might still have to tie wires back to somewhere else, depending on what amplification you're using.

This method can involve a lot more equipment and a higher price, depending on product selection. Everything is variable though, because maybe you have a source for power amplifiers at a steep discount or free for instance. Hiding such equipment in every single zone might be difficult or impossible.

There's definitely more flexibility with the centralized approach as for example, you can have audio in a hallway where you wouldn't necessarily set up a shelf with equipment.