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.
Tony Sirico was a colombo associate from the 1960s to 1980s before start acting.
Anyway in NY also the Luccheses are a strong family with the Gambinos and out NY I would choose philly or the outfit.
