Dans le New Jersey but à New York?

Thy, I don’t think it is the prepositions causing confusion here but differentiating New York City and New York State.

This is a situation in which the particular French use of prepositions adds specific information  - ‘ dans le New Jersey ‘ confirms the reference is to the state of New Jersey (which does have a city named just ‘Jersey’).

On the other hand, we have both New York State and New York City -  ‘ à (la ville de) New York ‘ indicates that it is New York City referred to, not New York State. The latter would correctly be referred to with ‘ dans l’État de New York ‘. 

https://www.lawlessfrench.com/vocabulary/usa-states/