DNP, does it matter the school?

What is your goal with the program? Is it a personal goal, to gain a skill set, or as a qualification to teach? Unless there is a compelling reason to attend a particular program, I would recommend obtaining the most value you can for your education. This is usually achieved by finding a reputable state university. Many flagship universities offer the DNP. This may provide an option to obtain an affordable education at a well known school.

I would personally like to gain the skill set from the DNP and use it to teach.

Take a look at the University of Alabama system. They offer in-state tuition for the online DNP. They also have a good reputation. I personally would not pick an expensive option and doubt that the name of the school would make a significant difference. I guess the exception would be if you want to try to obtain contacts through the program to teach at that specific school.

I have taken a look at them and they are in the list of top options for me.

OP: This is a trick question. Right?

I don't think it really matters. As long as it is a reputable and accredited, who cares where you go.

Usually, a candidate has a resume that shows a progression of accomplishments, and the doctoral program that was attended is but one piece of a larger picture. I've sat in on many hiring committee's, and I've not seen any nurses that only have a doctorate and no other history.

If you're trying to capture a plumb position, a degree from a pedigreed school might capture attention, but only for so long, as the rest of the candidates attributes will either confirm or deny any preconceived notions that a hiring committee member may have about the candidate during the interview.

To answer your question: Not in a considerable way.