I went through the tedious download process via App Store. The row in the App Store Updates tab said Xcode was installed. But no sign of it in Applications folder.
When I go to the Purchased tab of App Store, the Xcode row has a button labeled "Install". So Xcode was not installed? OK, click this button. This just starts another 4 GB download. It seems that "install" means "download" and nothing actually installs.
What's up with the App Store? I poked around in the /private/var/…/com.apple.appstore folder but didn't see anything enlightening. I am now downloading the .dmg file directly from the Developer website. (Slow connection: 16 hr download!)
Best Answer
Download it from here: https://developer.apple.com/downloads/
Just log in with your Apple Account and download Xcode 7.2