You will pleased to know the cruise terminal is very close to the city, actually walking distance to time square.You will leave the terminal onto a busy road and all you need to do is cross the road and walk straight through about 8 blocks.Im not sure what you can do with your luggage as there is not any luggage holding facilities at the pier.Although right next door is one of americas famous battle carriers (name on the end of my tongue)which you can walk around and im sure the kids would find exciting.Im guessing if the ship docks at 8:00am and once you have been through the very lengthy us immigration process it will be at least a couple of hours before you can leave the ship. Some cuise lines do this process whilst sailing the day before so that all immigration is finished prior to arriving in a us port.
As you have your luggage with you its going to be very difficult to actually do anything, especially when you need to be at the airport at least 3 hrs before your flight.Depending on which airport you are flying out of i would give yourself a good 45mins to get out of the city and through the busy city traffic.As with all fly cruising it is a good idea to give yourself an extra couple of days in the city you are flying from.It is a lot less stressful and gives you a great opportunity to explore.
Have the cruise line not arranged a "day room" for you? Otherwise just get to a 4/5 star hotel and tip the porter to leave the bags. Alternatively you could use the Grand Central Station's left luggage and take a opentop bus trip or the boat round manhatten but remember thet flight checkin will be 3.45 and so you will not have a lot of time after you have got off the boa.