Taking Greyhound to Florida?? Loooong trip from NY!!
By surrounding Islands I guess you mean the other boroughs of NYC. I am no expert, but there are parts that are better than others. I would stick to Manhattan for sightseeing, theatre, etc. . You could see a baseball game in Flushing, Queens (The Mets) or a game in The Bronx (Yankees) There also is Flushing Meadows Park an old World's Fair site that has a zoo, science museum and stuff like that. It is on a subway (tube) line #7. Outside of the city we have a great beach named Jones beach which is avaialable by taking the LIRR (Long Island rail Road) or by car.You can sometimes see dolphins there, but ususally later in the summer.
I will be in Disney World, so I won't see ya in Miami.
Safe Travel and let us know the trip goes. I am in Chatterbank a lot, so I'll see you there. I'll check here later if you have last minute questions, I'll try to help.