I enjoyed both Takayama and Hiroshima, but seeing as you've booked Takayama I won't comment on Hiroshima
I've been to Takayama twice, the first was in 2010 and then again last summer. In 2010 it didn't seem like it was a popular tourist spot; we didn't see any other foreigners, however last year it was filled with foreigners (well it was noticeable compared to 2010). They may have been there for the Takayama hand-held firework festival though.
There's a lot to photograph in Takayama, temples, traditional buildings, mountains, cult sites of worship, old traditional buildings, one funny statue, and the food!
You can see most of Takayama in a day, but if photographing then take your time and enjoy the two days.
Mountains near Hida Folk Village
Worldwide HQ of Sukyo Mahikari, Takayama. They offer a free saucer of sake on exiting the building. Quite a creepy atmosphere inside but quite cool to have a quick look.
You must try Hida Beef, it's expensive but it's the best beef I've ever eaten.
https://www.google.com/maps/place/郷...2!3m1!1s0x0000000000000000:0x8ddc0f51af3c9c88
Things to do in Takayama:
Eat Hida Beef
Try Takayama Sake (there's 8 sake breweries in Takayama all within a 1 mile radius, see if you can try them all like I did

)
Visit Hida Folk village
Walk the 10 mins from Hida Folk Village to Sukyo Mahikari it's an experience
Try sake icecream with real sake in it, there's one icecream shop that serves it with a warning not to drive afterwards!
There's a few big temples in Takayama, one of them 'cheat' with the goshuin and use ready-made goshuin.
There's two markets in the centre of Takayama the morning market is the bigger of the two.
Try and find the 'Golfer' statue (Hint: it's near the Hida-Beef restaurant) You'll know you've found the statue when you see it

Not many locals seem to know of it though.
Kanazawa
I visited there last year also, very nice place to go. The main place to see in Kanazawa is Kenrokuen Garden, it's one of the best gardens in the whole of Japan. Other places to visit while there are the food market, Kanazawa Castle, and the 21st Centuary Museum of Contemporary Art (I didn't think I'd like it but was pleasantly surprised.
Kanazawa Station - the entrance is shaped like a Torii Gate.
Kenrokuen Garden
And if you are wondering what a Goshuin is...
http://justburrus.blogspot.co.uk/2008/05/signed-and-sealed-memories.html
Not my blog but it explains Goshuincho very well.
As for taxi from Takayama to Shirakawa, the distance is 48km each way and the taxi driver will probably wait for you the whole time so you're paying for his wait time too no doubt. Both places are in the middle of nowhere

When you're in Osaka make sure to try Osaka Okonomiyaki