I'm heading out in just a bit so i'll try to add more a bit later, but to get you started:
July 4th - it's not going to be anything like your home town where you can bring a blanket and sit in the park... it's more likely going to be wall-to-wall people, some of who get there in the early afternoon in order to get a good spot. Depending upon your hotel room location you may have an excellent view of the large firework display that happens in Jersey City (at Liberty State Park). I'm not suggesting you head to Jersey City, but much of the Conrad faces the Hudson River and you may have a great view from inside the hotel (especially if on a higher floor). I would ask at check-in if you could have a room that might have a view of the fireworks... if you can get a good fireworks view from your room you may want to do that, if no view from your room then go with a backup plan, but realize it's going to be very crowded.
Walking Tours - my favorite recommendation is to take the A or C train to High Street (first stop outside of Manhattan, in Brooklyn). Walk down the hill, bypass Grimaldi's Pizza and instead go to Julianna's (both will have a long line, you can google the history between the two, but given the long lines i like to get there just as they open so that we walk right in and don't have a long wait). Afterwards, you can continue down the hill to the water and get the kids (and yourself )dessert at the Ice Cream Factory. From there finish your cones/sundaes on the water, or walk while licking your cones, back towards the Brooklyn Bridge and walk the bridge back to Manhattan, taking in the Skyline view (and the Statue of Liberty) as you walk the bridge like a local New Yorker... just remember to stay on the correct side of the path to not get in the way of the bicyclists who often come speeding past.
Economy Candy - 108 Rivington St
lots of old time candy, bulk candies, novelties, etc... good prices (definitely try the dark chocolate covered graham crackers)
Roosevelt Island Tram - nice way to see the city skyline all for the cost of a roundtrip subway ride
Coney Island - it takes awhile to get there (figure an hour on the subway) and it might be fun if that's your thing and/or your kids like amusement park rides... to me i'm more fascinated that there is a 'real' beach just outside of Manhattan than i am enamored by the rides. I don't think many tourists necessarily make out this way as there are too many other things to do closer to (or inside of) Manhattan vs. the time it takes to get to Coney Island (but again, if beaches and/or an amusement rides are your thing, it something to consider doing)
Statue of Liberty - if you want to see Lady Liberty and don't want to make a whole day out of visiting the island, the Staten Island Ferry (free) travels right past it making for a good photo opportunity. On the ride from Staten Island back to Manhattan i like to see at the front of the boat as we approach lower Manhattan. Great time to do this is to plan your trip so that you're returning back to Manhattan at dusk just as the lights of the skyline begin to illuminate, yet still bright enough outside to see things.
Sailboat ride - once a summer we like to take THIS COMPANY'S saiboat ride from Chelsea Pier to the Statue and Liberty and back. Not as much a fan of their 'yacht' and 'architecture' tours, but we LOVE their sailboat rides (Adirondack or Schooner)... pull away from the dock and my stress is just left behind. However, know what this is... it is not a touristy sailboat ride pointing out the NYC sights, it's a relaxing trip with little narrative; just a great way to see the city from the water (ie- as an example, on one our trips a few years ago, we are approaching the statue of liberty and captain gets on the microphone, "if you look to your right you will see the Statue of Liberty... this concludes the sightseeing section of this trip").
... and previously mentioned in a post above: Adrienne's Pizza Bar
Questions / Comments??