This is intended to be an academic question. All practical halachic questions should be decided based on a consult with your local Orthodox rabbi.
Pokestops are locations in the real world where you can collect items and pokemon eggs. They are kind of like geocaches. They self replenish. They correspond to real life objects, like murals or memorials.
My question is: Is one allowed to use Pokestops that correspond to churches? You don't have to be inside the church to use the Pokestop, but you have to be close to them.
Possibly relevant: I asked a poseik whether I can adjust a watch to the time according the bells of a church's clock. He said it is allowed mi'ikkar hadin (by the strict letter of the law), but I should treat it as a davar meguneh (something very distasteful).
Edit: clarification about the clock question: He said that using sound this way isn't really hana'ah. I would think this is similar, that it's not really hana'ah, so I doubt it's assur. But this but not even be a davar meguneh, as it might not have anything to do with the church per se.