Getting a physical tour of any of the numerous Microsoft Azure Datacenters across the world, either for yourself or for your customers, would normally be extremely difficult. However, Microsoft does arrange such tours (but rarely) for promotional/marketing purposes, which are geared for select strategic audience.
But you can always take a “modest” online Virtual tour of an Azure Data Center in Quincy, Washington, US. This tour will give you a high-level Idea about how these datacenters look like, and various facilities they Internally manage like Power, Cooling, Servers etc. As you enter each datacenter room, a narrator will provide a brief introduction. Use the in-scene hotspots, navigation and sensory feedback bar at the bottom of the screen to see more details.
You can access the Microsoft Azure Data Center Virtual Tour from here: Microsoft Azure Data Center Tour