Ahhh your first... so you get to experience how life changes with children
I would love to leave for a week to go on this Jamaica trip but I know we won't do it. I haven't ever left my kids for that long. I am thinking 4-5 days. I know I will miss them and my youngest will have a tough time with it.
NY is another place I have never been and would love to go.
Yeah, we know our lives will drastically change once the baby is born. Luckily, we're a little older than many parents having their first baby so we've experienced a lot of fun in our lives and we're ready to "settle down" and be parents now.

We know we'll still have fun but now it will be a much different kind of fun.
One thing to keep in mind about Jamaica is that the airport is going to be about 1.5 hours away (maybe a little more) from the resort. For that reason, we tried to get the earliest flight there and the latest flight back. Otherwise, two days will be shot travelling by the time you get through customs and all.
As for NY, there are a ton of things to do and 4-5 days would be plenty of time to really relax and enjoy yourselves. Take in a broadway show, take a cruise around the Brooklyn Bridge & South Street Seaport (goes by Ellis Island & the Statue of Liberty), check out the museums, go to central park (during the day), go to the Bronx Zoo, great shopping & night life. Just walking around Times Sqaure at night is a great experience - so beautiful with all the lights. Of course, all the bars & restaurants are open late there if you're night owls.