If we have a provider profile with the city as New Jersey, but no other information (nothing in the location field other than 'hotel') and we need to map it to a specific city what would be your suggestion for: North NJ, Middle NJ and South NJ?

The Trenton/Princeton area and environs should be "central NJ."

I could attach it to new Brunswick since it's smack tab in the middle of the city and it would be equal distance from clients in south or north NJ.

Since you are trying to solve for ONE provider who mistakenly used New Jersey as the city, rather than guessing, why not just contact that provider and ask her where she belongs, in what NJ city?

North NJ in my mind is Secaucus /Meadowlands which is ten minutes from the Lincoln Tunnel  or Parsippany/Wayne/Fairfield which is where a lot of hobbyist live which is 25-30 minutes from the city.
Central NJ is Edison/ Princeton/ Newark Airport where most of the general public works
South Jersey is the Jersey Shore I personal think South Jersey is Atlantic City or Mt Laurel.

Many out of towners don't know to look at the NJ top 100 list and will only look at NYC or Philly, pending which city they travel too.

This state is tri-cameral...North Jersey (which includes any ads that say Newark or Meadowlands) are part of the greater NYC metro area.  Ads that say Woodbridge or Edison are borderline North/Central Jersey.  New Brunswick, Trenton, Princeton, Monmouth and Ocean County shore locations are Central Jersey.  Areas near Camden (across the Delaware from Philly), Atlantic City, Cape May, and in the general vicinity of Philadelphia are considered South Jersey.  

As someone suggested, you could contact the provider.

I travel the whole state for outcalls , so it doesn't really matter to me but if i can help i sure will

I agree
Princeton should be centeral nj nt south  and no way should Rutherford be NY boards omg . Any time you cross a bridge to get somewhere it should have its own area on the boards anyway.  
DC is that way.

Did Admin arbitrarily choose a city?  Or contact the party to learn what city they meant?

Please don't lump North Jersey in with NYC. That's the last thing you should do. North Jersey is from about Essex County and up (north). To the east, the cutoff would be the Hudson River. I believed someone mentioned just allowing the city to be used. That would be great. No confusion with that one.

Add Cherry Hill to SJ and you`re spot on