Note: the event begins around 6pm when the ships depart their berths and hit the harbor. Fireworks will be between 6:45 and 7:30.
Battery Park: This will be the most packed area for viewing the Royal Rendezvous, but it will be the best of the free options as you'll be able to see all three Queens in the harbor, plus the fireworks. You can stay at park level or on the Esplanade and get right up to the waterfront, or try the raised outdoor deck on the right side of the Staten Island Ferry Terminal. Wherever you are, be dressed very warmly; this is not a quick event and it will be dark and cold when the fireworks go off.
The West Side Piers: They'll be windy for sure, but if you've come prepared with a drawstring hood, gloves and assorted other winter accessories in addition to a warm coat, you'll be fine. You won't be able to see the Queen Mary 2 leave from her Brooklyn dock from here, but this is the most convenient option with the most personal space. Plus, you'll definitely see the newest addition to the fleet, the Queen Elizabeth; both her and the Queen Victoria will cruise by right in front of you. There are publicly accessible piers at the ends of West 26th Street, West 19th Street (Chelsea Pierswalk out around the golf driving range), Perry Street and Christopher Street.
World Yacht's Harbor Cruise: Board at 5pm and sail on the harbor for three hours from 6-9pm. You'll be on the water for the fireworks celebration, and then your boat will follow the three Queens into the Harbor as far as the Verrazano Bridge, before returning to Pier 81. There's a full dinner served onboard (see the menu here) and it's $106.55 per person.
For more info, here's the official Cunard site on the event.
Know which ship you're looking at:
Queen Elizabeth: (the newest one)
Queen Mary 2:
[Video: Jaunted; photos: Wikimedia ]