I haven't been to Jamaica since college, almost 30 years ago, but I can't believe the diving is getting better. It sucked in 1980. Unless your standard is a lake or a quarry somewhere--in that case diving in Jamaica is great. But for the same trouble and expense of flying to Jamaica there are a lot of other (better) options in the States or the Caribbean, so those should be the basis for comparison.
NYC is the safest large city in the United States, and Manhattan is the safest part you're likely to visit. You'd really have to work at it to get into trouble there.
As you so clearly point out, your impression is three decades old. My impressions are based on trips in 2003 and 2008, where we saw a measurable improvement between the two in reef health, both animal and vegetable.
And I used to work for a company whose headquarters were on State Street, just across from the Staten Island Ferry Terminal, and you couldn't get me back there on a bet (and that was less than ten years ago, and I can't believe its gotten any better!).
People who come to this Board are looking for current information, not dated impressions.