If you choose Alfred over Spotlight, it looks better without menu bar icon. Paste the code below into Terminal.app and enter your admin password.

To Hide Spotlight Icon

sudo chmod 600 /System/Library/CoreServices/Search.bundle/Contents/MacOS/Search && killall SystemUIServer

To Show Spotlight Icon

sudo chmod 777 /System/Library/CoreServices/Search.bundle/Contents/MacOS/Search && killall SystemUIServer