Some jurisdictions require licensing/registration if you are "providing services in" their jurisdiction regardless of whether or not you have an office there. The only way to find out for sure is to call the appropriate agencies and ask.
In my state (Washington), many of the local cities require business licenses if you are providing any type of service within the city limits of that particular city. A friend of mine operates a plumbing business and has at least a couple of dozen different business licences on his office wall.
This is the kind of thing where there are really two answers; the legal (technical) answer and the practical answer. If you call the jurisdiction and ask, they will likely tell you that licensing/registration is required. On the other hand, many consultants do assignments nationwide without obtaining local licenses and seem to get away with it just fine.
If you are a corporation or LLC, you`re probably required to register as a foreign business. Check out the New Jersey Secretary of State`s office and/or Department of Licensing.