My wife lived in Nepal (foreign country) on a VISA from January to June 2016, would we file a partial year resident return in AZ, or a regular AZ state return?

The answer to your question is actually reasonably clear.  From the point of view of the Arizona Department of Revenue, your wife was only "temporarily" absent from Arizona while in the country of Nepal, and thus remained "domiciled" in Arizona for income tax purposes.

The only way to get around that conclusion would be if your wife took all of the necessary steps to demonstrate a permanent abandonment of her Arizona tax domicile in favor of Nepal.  This would include, among many other things, applying for citizenship or permanent residency in Nepal (a simple visa won't do for this purpose); obtaining an Nepalese drivers license; buying a home or renting an apartment in Nepal on a longer-term lease; transferring all of her financial affairs over to Nepal (bank accounts, etc.); selling her (your) Arizona house or permanently leaving your Arizona apartment; showing no intent to ever return to Arizona, and other such factors.

It is highly unlikely that she could meet the many burdens of those various test criteria . . . if for no other reason than that an intent to return to Arizona is demonstrated by her repatriation to the United States.

In other words, legal domicile for tax assessment purposes is quite a difficult thing to break.  The Arizona Department of Revenue has more to say on this topic specifically, which can be read at the following link:

http://overseastaxservices.com/wp-content/uploads/2014/01/AZ-residency.pdf

Thus, it would be my conclusion as a CPA (as would an Arizona auditor looking at the same set of facts), that your wife is a full-year Arizona resident for income tax purposes, despite a physical absence while on a Fullbright Fellowship in Nepal.

As to the overall taxability of her fellowship income, you may read more about this at the following AnswerXchange thread:

https://ttlc.intuit.com/questions/3664768

Thank you for asking this important question, and I am sorry if this answer is something other than what you were hoping to hear (regarding the ability of Arizona to tax your wife's fellowship income).  But at least now you have the true facts, and can proceed forward from there.