Well, there are Shinkendo dojos in Pheonix, Mesa, and Gilbert. And I know that Shinkendo's founder, Kaiso Toshishiro Obata visits Arizona frequently to instruct at the dojos in that state. So, if she is interested in studying a Japanese style that puts a heavy emphasis on function you might want to pop down to the local dojo there in Mesa and see what the instructors have to offer you.
http://www.azshinkendo.com/
Here are links to other Shinkendo dojos in Arizona:
http://www.azbudokan.com/
http://www.karateaz.com/shinkendo/shinkendo.html
As far as the Japanese styles go, one usually studies what is available...few places are lucky enough to have choices in swordsmanship. I know I have been dying to learn some of the western styles but the nearest competent instruction is a 3 hour drive from where I am.
Tell her good luck for me. And remember, the addiction to using swords can be tough on the wallet. Once you start it is hard to stop and they are like peanuts. You can't have just one.

Seriously, some of the best moments of my life have been either at the dojo or working with guys who make swords. It's a rather cool brotherhood in general. Fun is an interesting concept when we are dealing with 3 foot razor blades. In my experience, first comes discipline and understanding and experience. Then the fun begins. Be careful about enrolling your daughter in any school of swordsmanship that emphasizes fun and games.
Swords are deadly weapons. You wouldn't want your daughter studying pistol marksmanship from an instructor with a casual attitude about safety and discipline. It should be the same with swords. The fun comes with competency, IMO.
Brian