A lot of people would say Genovese just because of how organized and lucrative the family still is, but as others in here have said, if they even begin to think you're a problem, you're gone. The Colombo family has probably been the most accessible historically. Didn't some Colombos have a party a decade ago or whatever where Tony Sirico and other Sopranos people were right out in the open with made guys? I'd have to say they're the mob family to the stars.

"...the successful annihilation of organized crime's subculture in America would rock the 'legitimate' world's foundation, which would ultimately force fundamental social changes and redistributions of wealth and power in this country. Meyer Lansky's dream was to bond the two worlds together so that one could not survive without the other." - Dan E. Moldea