PhD application asking what other insitution I am applying to, how to answer?

Repeat after me:

“I'd rather not tell you.”

There is no really good reason for schools to ask what other schools a student is applying to. I personally make it a point as much as possible never to ask people who I'm interviewing or whose applications I'm reviewing what other programs they're considering. I do ask, however, if they are actively considering other options, this is something that can affect our internal decision-making process, so I ask if students are entertaining offers, but not where.

Schools are likely to be using this answer to gauge what schools you're applying to, with a view towards planning whom to admit. But again, I do agree that this question is invasive, and isn't really necessary. In addition, schools shouldn't be checking up with other graduate schools about their admissions, so I would answer in whatever way you feel comfortable.

Moreover, you can always claim that your answer was accurate at the time, but changed following the point at which you submitted the application.