Live in NJ conducting business in NY
In this case, it would really depend on the nature of the business you are conducting. For example, if you are only coming to New York to meet clients, then you could do so using a New Jersey company. If you have an office, employees or are providing a hands-on labor in New York, then the company may need to be registered in New York.
If you would like you can provide me with the description of your business, and I could give you a much more accurate answer to your question.