Facebook Page & place
Facebook "places" are simply Facebook Pages that have a physical location set. Any type of Facebook Page (brand, website, blog, school) can add or remove a physical location at any time.
The only differences in features is that it'll obviously allow users to check-in, see friends that have checked in, add recommendations, and show up on the mobile app and other location-based sections of Facebook (such as city pages, which aggregate places within the city).
Facebook Pages
A Facebook page is the standard business page. It is an area on Facebook where companies can interact with the audience.
The page will allow your audience to like you. This means that your updates will appear in their news feeds amongst their friends updates.
Facebook will provide your page with insights. This is their name for page analytics.
It allows you to see your like growth, demographics of your audience, and statistics about your individual posts.
Facebook Places
A Facebook place has the same functionality as the pages; however it is aimed at the companies or organisations that have a physical location.
This is useful if your company is a coffee shop or estate agents where you want people to come into your store.
Additional options are available within the page admin; these allow you to specify your company location and state additional information, such as parking availability.
The most significant difference between a Place and Page is the check in functionality. This allows visitors to your location to say that they have been to your location through a mobile device.
You can use adverts that target people who have checked into your location or give special deals to those visitors.
When a visitor checks in, a message goes out on their news feed that lets their friends know they are at your location, this is a great opportunity to promote your business through the Facebook news feed, for very little cost.
Unfortunately, a place cant deal with multiple locations.
If your company is spread across different addresses, I would suggest you either create multiple places for each location, or combine all the places into a page (combining is the preferred option here).