Moving the NFL draft out of New York City has been talked about for years, however, nothing has ever come of it.
That may change after the 2014 NFL draft. Per, the New York Daily News, the NFL's deal with Radio City Music Hall expires after this year, with options for future years.
Because of that, the NFL will certainly explore the option of other host cities, and according to commissioner Roger Goodell (via Rich Eisen), multiple cities are already aggressively bidding for the right to host the 2015 NFL draft.
Just spoke to @nflcommish for Tues Night Draft Special -- says mayors of Chicago and LA very aggressive in trying to get the 2015 Draft.
— Rich Eisen (@richeisen) May 5, 2014
Chicago and Los Angeles are likely just two of many cities that could enter the bidding process if the league does decide to move the draft out of New York City.
The NBA moved its draft in recent years and the NHL currently has its draft on a rotating schedule, so the NFL moving their draft wouldn't be unprecedented among major sports. There have also been rumors that the NFL could explore the idea of holding the draft in multiple locations with each day of the draft taking place in a different city, though there would certainly need to be logistical issues resolved before such could happen.