Knowing the following would help in figuring out better parameters:
1. where is your work address in NYC (intersection would suffice),
2. what type of place are you looking for $2,3000 (studio, 1 BR, 2 BR, house, etc),
3. how much transportation budget do you have. E.g., if you have to take both PATH ($75 / M for unlimited) and NY Metro ($112), then it would be about 2x the price of just PATH. Or, maybe you can take the ferry, which is more expensive, e.g., $250 a month,
4. how much do you value living closer to NYC. E.g., you can live in near Exchange Place or Newport in JC, which will probably be the most expensive option for rent (and cost you extra for parking the car), but allow for 7-minute commute to the nearest Manhattan PATH stops (WTC or Christopher). Or you can live in Journal Square for 30% reduction in rent, but commute to Manhattan gets longer by 10 or more minutes, and area is not as pleasant,
there are some communities in Bayonne and farther in Jersey City which are more suburban and very nice, but commute to Manhattan gets longer by at least 15-20 minutes. however, you will have more of a suburban feel, and cheaper rent.
FYI, commute from J.C. or Bayonne into N. Brunswick will be at least 40 minutes each way.
I also represent a property management firm that always has apartments for rent and cover the realtor fees.
Call me anytime you'd like to talk, 917.209.9391
Please contact me and we can talk more.
Shoot me an email if you would like some more advice.