I promised myself no more gear! I'm on a 12 step program already, though am not doing so well.
We are here to support you, no one mentioned shopping at B&H, yet 
You mentioned you are going to be heading to Florida in a few weeks, not sure if that means you will be in New York the whole time or what travel arrangements you have arranged while in NYC. One thing to think about is getting a pass for the Subway for the time. Often the Subway will be easier (timewise) than Taxis and less costly, and grab a map. Not sure what you are into, some things people like and others may not like, but figured I would throw out general things and if anything is of interest, can go into more details.
On the diving side of things, there are various Dive Clubs that meet in NYC. One that I go to when I get a chance is the NYUPS - next month is pushed back to the 14th though due to the Labor Day Weekend, so it may be too late for you. There are other clubs also like the Sea Gypsies who have something on September 8th.
As mentioned, there are many great museums - The Museum of Natural History and The Museum of Modern Art and the Metropolitan Museum of Art are three of the well known ones and are good.
Then there is food and bars. As you would guess there is a ton of variety, from Steakhouses to Vegan. Pretty much anything you want. In your neck of the woods (Lower Eastside) great Delis, and also Chinatown/Little Italy. I used to go to there often - grab food then cannoli and espresso afterwards. (Not when I say in your neck of the woods, it is fairly close and would often walk things even if 15 minutes or so.) Lot's of great music clubs, everything you can think of. Jazz, Classical, Rock, whatever with venues ranging from the hoe in the wall to Lincoln Center, Madison Square Garden and Radio City Music Hall. Broadway shows...
There is the Seaport which is a good place to go to for a bit. There is a ton of stores, such as Macy's, which you may have seen in movies and alot of locations used in movies. There are tours that around sites. Used to be a Seinfeld one, for instance. There is the Statue of Liberty (which I never went to my entire life, and finally went to when friends came in from out of town, and it was worthwhile) and Ellis Island (where immigrants came into the U.S., also interesting.)
If you are into sports, baseball season is still on. Yes, I know, but when I was in Australia I started getting my head around Cricket a bit during those couple of weels, and when my friend and his family came here, we went to a baseball game and they had a blast. Actually took a few people from Australia to games and they had fun.
If you have time to wander a bit outside of the City, within 1-2 hours in any direction there is alot to see on that is non-City. There are places to dive, like the Quarry in PA, which is about 1-1/2 hours away and things off of Long Island.
Really could write a ton more, but figured would throw a few things out there. Lived in the City for many years, now live a bit outside of it. About 30-40 minutes drive, with non-rush hour traffic of course 