I recently moved my Xcode (4.6.2) from /Applications to /Users/daniel/Applications (I'm getting ready to slim down the main system partition to use an iSCSI target for my home folder, and want as much on it as possible).
The link in the comment by Buscar above isn't valid for new Xcodes that come through App Store. Instead, just move the app using Finder. You'll probably be asked to supply your credentials (due to admin permissions on some of the files inside Xcode.app).
You'll notice at first that Xcode starts up as if nothing happened. All seems to be well, but isn't quite, though — your Command Line Tools will be fudged. Other stuff that depend on it, like Homebrew, will fail unless you do this:
In Xcode, open Preferences and go to the "Locations" tab. The dropdown labeled "Command Line Tools" will be blank and there'll be a warning sign next to it.
Simply select the Xcode in that dropdown, and after once again supplying your credentials, all is well :) Even updates will perform as expected (I updated to 4.6.3 with no issues).