Your work would likely be in Manhattan, maybe in Brooklyn. A 2 bedroom apartment within walking distance of the business districts in midtown or downtown runs about $4,000 a month. 3 bedrooms are available on the Upper East Side, but at that range prices rise exponentially. The only good public schools in the city are the magnet schools.

Obviously $8,000 on an apartment isn't supportable on $100k. The compromise most people make is to commute from New Jersey or Westchester (45 minutes to an hour, depending) on the excellent train network. If you're coming from Westchester, this is a very comfortable commute on relatively new trains with WiFi, etc. Schools in these places are very good, and leasing a 3 bedroom house in that range is very doable.