We sailed last year on that same weekend on the MSC Meriviglia . After lots and lots of research, we decided to fly in the day before [instead of driving from Massachusetts]. We stayed at the New York Marriott at the Brooklyn Bridge - and had no problems at all. It was expensive, but worth it. There were a lot of people checking into the hotel with their bikes.
But the good news is that the morning of the race, we pre-arranged an Uber pickup @ 9:30 to the Brooklyn Cruise Port and had no problem at all getting there, in fact, the driver took us on streets that had no traffic and, other than at the hotel, we never saw a bicycle that morning.
If the route is the same this year, I would highly recommend that hotel, and leaving early to beat the spectator traffic in the area. It was well worth the extra money for peace of mind.