Ray J isn't backing down from challenging Mario in a singing battle ... despite his opp not taking the competition too seriously. We caught up with Ray in NYC mid-morning Tuesday, where he was advocating for a TMZ After Dark and Brunch Tours in the Big Apple -- a move which definitely has a nice ring to it. After all, Ray has become quite the Hollywood draw with our bus patrons, so an expansion may be on the horizon!!! Back to the matter at hand ... Mario and Ray are currently in a volley of