Chureito Pagoda (Yamanashi Pref.)
I feel like Chureito Pagoda is a bit of a triple threat when it comes to amazing pictures. Views of Mt. Fuji (on a clear day!) with a pagoda and cherry blossoms if you time it right?! I don't think you can get more quintessentially Japanese than this. I've been to this pagoda twice (I live just a little over an hour away from there right now) but haven't made it there during cherry blossom season before - I have heard that it does get particularly busy around that time of year though. Bear in mind that it's quite a few stairs to reach the pagoda - it's worth every step though when you get to the top for that view. If you do want to go to Chureito Pagoda, try and schedule it in for a day when the weather forecast is going to be clear. On one occasion when I went here, my sister was in town but sadly the weather just didn't cooperate for us at the top and we couldn't see Fuji!
Miyajima (Hiroshima Pref.)
Aside from being one of my most loved spots in all of Japan, Miyajima has a number of amazing Instagram-worthy picture spots. Itsukushima Shrine is one of the best! You may have seen pictures of the iconic floating torii gate that you see above - it makes for great photos, and if you stick around all day like we did when we visited, you can get pictures of both high and low tide with the torii gate. Plus, if you're wanting to see wildlife to photograph, there are a ton of deer around Miyajima too (it's not just Nara that is a haven for them!)
Hitachi Seaside Park (Ibaraki Pref.)
Higashi Chaya (Ishikawa Pref.)
If you want some pictures with a true "step back in time" feeling, I have to point you in the direction of Higashi Chaya, in Kanazawa (Ishikawa Prefecture). This particular area was a geisha district of the city, and has been preserved so that you really do feel like you're in a different era. The traditional looking shop fronts with their beautiful wooden paneling makes for wonderful pictures - plus, an added bonus is that some of those shops are teahouses and stores where you can stop into!
Jigokudani Monkey Park (Nagano Pref.)
There's something incredible about this place - it's like having a real life interaction with a National Geographic magazine cover. You can get up pretty close to the snow monkeys, but the park rules and regulations do advise you to use common sense and especially to avoid looking the monkeys in the eye (it can be perceived by them as an act of aggression - they are stil wild animals after all). You can get some amazing shots though of the monkeys bathing in the hot springs, and they just tend to go about their days as if the hordes of visitors aren't there watching them!
There are so many more places that make for brilliant pictures, I'm not even starting to scratch the surface here with my 5 recommendations - but they are ones I have visited and thought very highly of! I hope if you are planning a trip out to Japan that you'll get the chance to visit some of these iconic spots and that you'll have pictures you will cherish for a lifetime.