I wrote my message in haste as it towards the end of my lunch break. I forgot to write about credit.
I would strongly suggest that you get a car even if you live in the middle of Manhattan. When you have two small children and it is 105F with what feels like 100% humidity you will need to drive places.
The issue I had when moving over here is that your credit is zero and once you get your drivers license (they don't recognise an international drivers license) you have zero years of driving experience. This means you can't lease or finance a car at a reasonable cost. If your husbands company have not included a car in his contract it would be a very good idea to go back to them and ask if they can lease a car for you or at least co-sign. Whatever you do, don't cycle on the roads in Manhattan!
Also, if you don't have an american express card already I would get one ASAP. Amex are great because they will transfer your credit card to the US. This will give you some sort of credit rating. Again, when it comes to renting your apartment, be prepared to pay 3 to 6 months of rent upfront plus one months deposit. Ideally your husbands employer will be able to co-sign so you can avoid this.
The reason for my aversion to Manhattan is that high rise apartment living isn't for me and my husband and I have not amassed enough yet for a townhome. I lived on the UES as a child and we were on the 37th floor. Sometimes it took 20 minutes for the lift to arrive. When you have two kids, a pushchair and your shopping to haul up it can be a pain the rear.
Also, apartments here are nearly all rented as unfurnished. Areas to avoid are anywhere north of central park, above 95th on the east side and 110th on the west side. Tribeca is lovely as is Gramercy Park, Soho, the villages and the UES is good if you can find the right apartment. I would avoid midtown, battery park (dead at weekends and a bit noisy/dusty due to the WTC rebuild) and anything a block from FDR drive, the west side highway and the entrances to the bridges and tunnels.