Also, driving distance is another concern. During my younger years, my parents would drive me to lessons. The three teachers I had over the course of my childhood were all located within a fifteen minute drive of our house. For people who can afford $40/hour lessons, I'm assuming they don't live in shabby neighbourhoods. It may be helpful for you to live relatively close to your students.
+1. I have walked to lessons, and I now send my kids to stuff like this. My #1 rule for Generic Decent Kid Activity is that it has to make my life easy.* I chose the orthodontist my DD can walk to after school, the tuba lesson a block away, the karate lessons 3 blocks away, the school clubs on the days when the activity bus runs, etc. etc. etc.
Sure, if my kids were going to be auditioning for Julliard, I'd suck it up and drive them to the best teacher I could find. But that's not my kids. And it's also not your target audience -- I am. People like me, whose kids don't have any special musical talent, but who think music is a good idea for their kids to learn, and piano sounds like a good baseline, and gee I'd love to fit this in if it's cheap enough and I can find room in the already-busy schedule. I don't need perfect, I need "good enough." And I have plenty of those in my town -- so why would I even look at people farther away?
Note that this doesn't necessarily mean you need to be in a rich neighborhood -- I think people with a lot of extra money are likely to search out the "best" teachers and care less about convenience or price, so they are not your target audience, either. But I do think that a borderline-sketchy neighborhood won't serve you as well as a solid MC one would. Sorry.
*OK, I lied -- #1 is that it has to be reasonably priced, but "easy" is a very close second.