You might have heard about that new Batman vs. Superman movie over the weekend. The word is that it's not very good, but the new Batcave designed for the film is really impressive. You can now explore Batman's lair in Google Maps Street View, and in 3D with Google Cardboard.
The standard Google Maps Street View location is available from this link. That should work on any device and let you poke around. To get to the Batcave in Google Cardboard mode, the easiest way is to pull it up in the collections area of the Street View app. There's a handy Cardboard button right at the top of the app.
The space to explore inside Wayne's house is huge. You begin in the regular "house" part, then venture into the secret Batcave. There's the Batmobile parked near the entrance, then you can go into the armory, workshop, and more. The path you take is a little awkward, but you'll find your way around easily enough. Oh, and in case you were wondering, Bruce Wayne lives in Orion Charter Township just north of Detroit, according to Google. I don't think that counts as canon, though.