I haven't noticed exactly when it happened but previously I was always using spotlight to run Xcode. Now if i'm typing "Xcode" in it, only folders containing this name show up, or some xcode projects, not all though. I've tried search in finder and even choosing kind of files - Application, still no luck. Did Anybody face this problem before?
Try Rebuilding Spotlight index. You can do it from the Terminal:
$ sudo mdutil -i on /
After upgrading from El Capitan to macOS Sierra I had the same problem.
The only command that did the trick was:
sudo mdutil -E # from mdutil usage "Erase and rebuild index"
If that one doesn't work directly, try running this command first:
sudo mdutil -i on # from mdutil usage "Turn indexing on or off"
Updating the permissions did the trick for me:
chown -R $(whoami):staff /Applications/Xcode.app
Suggested from here: https://forums.developer.apple.com/thread/82503