Advice needed: buy a house/condo in NJ/NY metroplitan area

I started working in Manhattan since 7 months ago. I plan to buy a condo or a single family house. I have two kids, one is 3.5 year old and one is 1.5 year old. The maximam I can afford is 680k.

I am not familiar with the NJ/NY metropolitan area. I would consider the following factors:

1. School
2. commute/transportation convenience
3. property tax.

Where should I buy? Should I buy a codo or townhome or a single family house?

Thanks for comments and avice.