Generally, a legal document will be governed by the law of the jurisdiction where the actions of the parties will be performed. This is generally the place in which the parties to the agreement reside or where the property is located or the service is performed, in your case that would be your State where you are performing the work.
The location of governing law is important to you because it directs that the parties agree that any claim will be governed by the State in which you live in addition to bringing any claim before the Courts to one located in your State. So, in your case that would mean that the laws of Arizona and the United States would govern the contract and they agree to bring any claim before the courts of Arizona. This is important primarily because it is impractical to be familiar with the laws of foreign jurisdictions and would be expensive, inconvenient and possibly impossible to enforce in a foreign jurisdiction.
It sounds as if she wants a ‘neutral territory’ to rule out any imagined ‘home court advantage’ but this isn’t to your benefit and the fact that she is even suggesting it makes me concerned about what kind of client she will turn out to be.

The location under which you are signing the terms of the contract should be one that is convenient to you because if there is a dispute, you may well have to travel to the Courts to settle the dispute and if you were to choose such a location such as Switzerland, it may well be impossible to enforce not to mention expensive and inconvenient.
There are cases where the parties will agree to the laws and courts of a jurisdiction that is midway between the home jurisdictions of each party because it then places an relatively equal burden and benefit on both parties but it doesn’t make much sense unless the jurisdiction selected has some kind of reasonable connection to the transaction. For example, Wichita, Kansas can be viewed as midway between Phoenix, Arizona and Toronto, Canada but do either of the parties have any connections to Wichita?? And if this location is selected and a disagreement arises and it ends up in the Courts of Wichita, they may well refuse to deal with your issue in their Courts on the basis that neither of you have any connections to Wichita.
The bottom line is unless she is a lawyer, she probably doesn’t understand how these contracts are generally drafted and it isn’t to your advantage to agree to another jurisdiction based upon her lack of understanding. My last piece of advice is that none of the above constitutes legal advice and you should always consult a lawyer in situations such as this.