When in Coney Island, you have to stop at Nathan's Famous, home of the hot dog, although they sell other things. Eating a Coney Island knish can be a serene experience. If you like roller coasters, there is the Cyclone, which opened in the 1920's. It's on the National Register of Historic Places. I don't indulge in roller coasters, but it generates a lot of screaming. The Aquarium is nice, but not quite up to the standards of the National Aquarium in Baltimore.
The Bronx Zoo and NY Botanical Gardens, also in the Bronx, are great. You can get to the Zoo by express bus from Manhattan or by subway, and the commuter railroad goes up to the Gardens. If you like cemeteries (I do) one possibility is Woodlawn in the Bronx, which is home to the massive mausoleums of the American Robber Barons.
The Staten Island ferry is a nice cheap ride, with a great view of Manhattan Harbor. You get it at the bottom of Manhattan Island, and can just stay on the boat and go back to the city. There are a few interesting things in Staten Island, but they are not near the ferry stop. (Richmondtown Restoration, a tibetan museum.) The Ellis Island restoration is also more interesting than I expected it to be.
If you like art, forget that it is a major tourist destination and go to the Metropolitan Museum of Art. It is one of the world's greatest collections of 1,000's of years of art from all over the world. The Frick Museum on 70th and Th Avenue (10 blocks south of the Met) is an often overlooked diamond: it's a private mansion that was turned into a museum to house the art collected by its original builder. They have 3 of the 35 paintings agreed to have been painted by Vermeer and 5 Turners, as well as a gorgeous portrait by Ingres.Paintings have been added over the years, but always in small measure and in complete consistency with the original collection & ambiance.
The Empire State Building is probably it in terms of views, unless you go to a restaurant, but none of those are anywhere near as high as the ESB. My brother visited it with his GF in May and it took them several hours to get to the elevator and then they had to wait for an hour to get back down.
Does the NJ hotel run a shuttle service into the city? If it does, then you should be okay if you can get rides back until late into the evening. If it doesn't, driving is a hassle & parking will be very expensive if you cannot park on the street. If they are on a commuter bus line, it probably would not be that expensive to go back and forth, but you'll have to go back & forth thru Port Authority on 42 and 8th, which is pretty out of the way. Does the hotel website indicate the commuting options? My brother stayed in a hotel on 27th & Madison, which he said had reasonable rates and which he was very happy with. I can check the name with him. Even if the NJ place is offering a very large room, unless you need it for the number of people you will be traveling with, consider that you won't spend too much time there all in all.