We are staying at the Millennium Broadway hotel, will our best bet be to get a yellow cab out to the terminal or is there some other way that would be better? Roughly how long will it take and how much will it cost?

Yellow cab or another car service are the only ways. It is not convenient otherwise. Time depends on time of day. And it will be faster to spring for the toll at Battery Tunnel rather than take the Brooklyn Bridge.

I would reserve a car service so you do not have to worry about waiting for a cab and have a fixed price. Go to web sites of Carmel and Dial 7 for coupons.

I'd price a car service and see what they charge. I have no idea. I suspect it will be about $50 from that hotel. You can also take a taxi, which will likely be less, though UberX might be your best bet.

You don't say what day of the week. If it's a weekend, then there should not be too much traffic, but the Brooklyn Bridge always backs up on weekends, so that's where the bottleneck will be.

I used to regularly go down to Red Hook but have not done soit for about a year. There used to police monitoring the traffic toward the cruise ships and there was always a tie-up on those days.