We cruised on the Zenith from New York to Bermuda last year (Apr 03) and booked the Marriott Marquis at Times Square through our travel agent at a weekend rate of about $180. It's an OK area for safety and the hotel is very nice. You don't say what age your daughters are, but unless they are late teens and used to the city you shouldn't let them out on their own anywhere in New York unless they are used to the city. The hotel is a quick taxi ride to the port. If you are staying in New York on a weekend night your TA can probably get you a similar rate at a major downtown hotel. An advantage of this hotel is there is a large taxi entrance inside the structure at the ground level and its all very organized in getting a cab to the port.
When you arrive at the port, make sure your driver stops at the right terminal for the ship you are taking. Ours dropped us at the wrong ship and it was a long hike with all our baggage in tow to the correct one. (Two celebrity ships were leaving at the same time and we didn't specify which ship, which probably caused the confusion.) Compared to other ports we have used, this is a large, noisy terminal and can be confusing. If you are not sure of anything, find a celebrity check-in employee inside the terminal to help.
There will be porters just inside the terminal to take your checked luggage. But just to be safe, make sure they are celebrity employees - or contractors before releasing your luggage, and also if you're going to tip them you will need to do so at that time (They will remind you of that anyway). We thought it was worth a few extra dollars to make sure they handled ours right.
This is a wonderful cruise and the Zenith, although aging, is still a beautiful ship and a good size to enjoy on the ride to and from Bermuda. The stops at Hamilton and St Georges were entertaining. If you want to see the real Bermuda, buy a bus pass on the city bus while you're in Bermuda and ride around to Horseshoe Bay and then on the point, then take the ferry back from there to Hamilton. With the bus pass you can get off the bus whenever something looks interesting and get back on when the next one comes by. We walked from the bus to horseshoe bay, bought a soft drink at the beach bar at the big hotel there and relaxed on the pink sands of the public beach for a while. St Georges is also good to explore on foot (and shop) - walk up to the unfinished church and then on to the fort for some beautiful ocean views. If you have time in St Georges you can also follow the old train route up through the hills a way to see the homes and other views.
We will probably do this cruise again - after we've worked our way through our wish list of other Celebrity cruises.
Whatever you do, though you will have a good time!