I visited the shrine shown in Air. It's called Yaho Tenman-gū in real life and is located just a few hundred meters from Yaho Station, the nearest train station.
Image from Episode 1 - 17m56s
The shrine buildings are the only thing matching in this location.
Image from Episode 4 - 12m27s
This side entrance to the left is the same. Wasn't open when I visited though.
Image from Episode 4 - 21m00s
One of the Torii entrances to the shrine grounds. It doesn't really match, but I included this picture anyway.
Image from Episode 10 - 09m27s
A wider shot of the main shrine building. To the right you can see the head of a cow statue similar to the ones at the other Tenman-gū shrine I visited.
Image from Episode 10 - 09m38s
The saisen-bako is at the bottom of the stairs in real-life, and there's handrails instead of walls lining the stairs.
This location was visited on 2014/04/13.
Yaho Tenman-gū official website
Special thanks to the ones who went here before: