Your question has to do with what a state feels they can regulate, and what other states will recognize regarding regulation. I would recommend discussing this with a lawyer who can look at the specifics and give you real guidance. This is mostly a response aimed at ensuring you get as much from such a meeting as possible.
Additionally some of this is generalizable to international business deals gone bad as well because most of the issues are the same.
First I want to point out that in general if you have to go to court or even collections you risk creating a bad dynamic regarding future work. Additionally court takes a lot of effort on your part and it may not be worth your time unless it is a large amount. What going to court can give you however is a better position if your client declares bankruptcy. In court both sides lose, just one side loses more and you will never be able to bill for your time in preparing the court case. So unless it is a lot of money, my recommendation is not to go to court. BTW, a good reason for contracts is to minimize the times that court may be needed rather than actually making sure you can win in court. You should go in assuming you will not be able to collect all your attorney's fees and that you are investing a lot of time you will never be paid for. So take that as a big warning before you go to talk with an attorney.
So before you go you need to find out why they aren't paying. If they simply cannot afford to pay right now you have to make the decision as to whether to pursue a case in court on the theory that if they go bankrupt you can more easily collect, or whether to just hope they do better and can pay you in the future. If it is a contract dispute, if there is something you can do to make them happier and get them to pay you, that is better than going to court.
Now the key thing is that, in the US, states generally have the power to regulate businesses which do business in their areas. I say "generally" because a lot of things are outside of this. The reason is that the US Constitution vests the regulation of interstate commerce with the federal government, and this has long been interpreted to mean that states cannot impose barriers to business from other states. This is the reason why, absent Congressional action, states cannot collect sales taxes across state lines for example.
The two major issues I can see that you would want to discuss with a lawyer are:
Which state's courts can decide the issue. My immediate thinking is that since this is probably a payment dispute only, either state probably can. If there are other contractual issues however, this may complicate things. Also you want to check any contracts you have with your customer to see what the contracts state, and if you don't have a choice of laws/venues provision consider adding one in the future.
Which state's laws are at issue. Which state's laws are most favorable to you? If there is no choice of laws/venues provision this allows whoever files first to choose the venue which gives an advantage.
Are there any major reasons why the other state might decline to enforce a favorable ruling on your behalf? In the US this is less of an issue but it does occasionally come up. In international business this is a much bigger deal. In general if a ruling would be clearly and heavily against public policy (again absent Congressional action if between states in the US), a state court may decline to enforce it at home. (In International business dealings, states have much more leeway in deciding to do this btw, because the full faith and credit clause of the Constitution has no effect.) Again, in the between the states, this isn't likely to be an issue but it is worth looking at just in case.
You want to get your ducks in a row on these three issues before you file, and this means discussing all three with your lawyer. The reason you should make sure you bring them all up is because you want to make sure that you have an opportunity to discuss all these issues and get feedback. If you go to court, you want your attorney to be a collaborator, not the one simply in charge.
Once again, the above three generally apply to international lawsuits as well though the issues are usually more complex there. Keep in mind every jurisdiction will likely have its own ways of answering all three. Every state in the US, for example, has its own tradition of conflict of laws resolution and these apply roughly in the same way (aside from the Full Faith and Credit clause) to international lawsuits as well. I would expect similar in the EU between countries, or between a business in Argentina and a business in Wisconsin.
