If your going to want to do something like this your going to need some help. The three main things I use to find payphones are: Facebook, Reddit, and Google Earth (or streetview). I simply just got on my cities subreddit (they usually also serve pretty much the majority of the greater metro area) and just looked up "payphones". There were about 4 or 5 posts about them and I simply just copied the addresses into Google Earth, made sure they were still there, and went from there. Although Facebook was less of a help for Cincinnati, I did find the location of one and I'm sure it would be a better help for larger cities. To make the website I used my basic knowledge or HTML and used mostly W3Schools and Stack Overflow for specific questions I had.
Links:
Here are some links to the subreddits of major cities around the world.
US:
r/chicago
r/detroit
r/columbus
r/losangeles
r/atlanta
r/philadelphia
...and many more