I've been in your shoes. The best time to move is before you get pregnant with #2 or before your oldest child starts kindergarden. Before this, the school district (and the higher prices that go with it), is not a big thing.
These are the pros and cons of moving while pregnant, places to look near NYC, who to use as your mover, and what to do if your husband ends up with a long commute.
WHY IT MAY NOT BE A GOOD IDEA TO MOVE
You'll really need your husbands help when you are pregnant, as #2 is a lot harder than the first pregnancy as you will be looking after your child. You ae more likely to feel morning sickness, and fatigue will likely be worse, as you may not be able to rest as much during the day. Expect housework, ability to cook etc. to go down the drain if you aren't feeling well or can't go near a kitchen.
If your husband is working close-by he can help you when he comes home with either taking care of your child or helping around the house. He'll also (hopefully) be able to help you with at least one night feeding with baby #2. But not if he has three hours of commuting a day.
More importantly though, as your due date approaches you need your husband nearby in case you go in labor. You can't drive yourself to the hospital and there's no way you'll be able to look after your child. With #2, you will not have the luxury of time first-time moms do - labor usually lasts half as long and it becomes more important to be able to get to the hospital quickly.
IF YOU NEED TO MOVE, NO MATTER WHERE
Hire a good mover. I am very pregnant with a toddler and had "Arthur Werner" handle my move. They were fabulous from start to finish and are one of the few licensed to handle both local and interstate moves in the tri-state area (NJ, CT and NY). I would hire them again in a heartbeat. http://www.arthurwerner.com/
If the move is in NJ or NY, "Flat Rate" is also highly recommended. http://www.flatrate.com/
Ask about replacement insurance. It is optional but worth getting (about 1% value of household goods) and will give you peace of mind in case of damge. The standard insurance provided free of charge has minimum coverage and pays very little.
IF YOU STILL WANT TO MOVE AND WANT A NICE SUBURB NEAR NYC
If you want to look in NYC or near - Try contacting moms in the NYC area for up to the minute ideas on the best places to live - Baby Bites is an excellent online resource. I think you can post your question there too.
http://www.babybites.com/about/about-us/
This site provides great overview of things to do in NY and different neighborhoods.
http://newyorkkids.timeout.com/
New York magazine had an excellent article about this October 7, 2002 - "10 Suburbs you can afford" - nice neighborhoods, good schools, easy commutes. This might be a good starting point. (For links to each town with in-depth info on each please check my answer at http://www.mamapedia.com/questions/4972888158665506817 )
- Montclair, NJ - 29 min to Penn station
- Maplewood, NJ - 20 miles to midtown Manhattan, 25 to 35 min to Penn
- Katonah, NY - 46 miles to midtown Manhattan, about 1 hour commute
- Dix Hills, NY - 36 miles to " ", about 1 hour to Penn
- Montville, NJ - 33 miles to " ", about 50 min to Penn
- Ossining, NY - 36 miles to " ", about 48 min - 1 hour to Penn
- Pelham, NY - 17 miles to " ", about 29 min to Grand Central
- Larchmont, NY - 21 miles to " ", about 40 min to Grand Central
- Cold Spring Harbor, NY - 35 miles to " ", about 1 hour to Penn
- Milford, CT 66 miles to " ", about 90 min to Grand Central
IF YOUR HUSBAND WILL HAVE A LONG COMMUTE
Our offices were in NJ and my commute was almost two hours by train from CT. I was fortunate to be able to work from home full time through my first pregnancy- if your husband can arrange a similar arrangement it would be great. Co-workers (men) who came in from PA, sometimes with two hours commutes, soon were to exhausted to continue and decided to rent near their work to be able to afford a bigger home for their families.