This is an old question but there is a lot of conflicting information above, and much it conflicts with my personal experience living on Ikoma Mountain in 2000-2001 (at the time of this writing I live in Okinawa, and the situation isn't entirely different). I lived in front of a large shrine called 石切神社 in Eastern Osaka. (Oh! it has its own website now! (O.o) Times change...)
The shrine road through Ishikiri is the old-shop district for the mountain. It follows the track of a very old footpath which runs from the front of the shrine, up through the neighborhood above until the houses end, continues to ascend through a forest passing several active and inactive shrines, up over the mountain (which at the peak had an amusement park nobody went to -- I wasn't ever sure if it was in business or closed down), down into Ikoma City on the other side, following a very old Ryokan road as it descended. Along the way you see numerous temples, markers to things that are still present but no longer have paths, stone lanterns that no longer mark anything, statues, graves, disused, overgrown paths to other interesting and unmarked things, etc. Its pretty amazing if you actually take the time to go exploring.
Walking through this area makes it clear that the mountains and forests of Japan hold quite a few hidden secrets. I've followed a few of the overgrown paths on Ikoma and discovered some pretty interesting things:
- Huge ancient carved rocks where the letters have stretched out in the rock due to water erosion. (I found one where the letters have eroded two directions, meaning its been turned at some point between being carved and now. I always wondered what the story behind that little effort must have been -- the stone must weigh >10t and sits on a pretty rugged slope in a rather remote part of the forest.)
- Little statuettes lining the unused road that have almost succumbed to moss erosion -- one of which was being actively cared for by someone who had dressed it and periodically cleaned around it and its little partner. (Why? Who? How is this one special? They all look the same...)
- Obvious intersections that lead who knows where
- Graves or monuments of once-famous people.
- Etc.
Researching these things is pretty much impossible without just stomping around in the woods. I would never have known these things existed just outside my neighborhood were I not the type to take long walks through through the forest. The girls at one of the shrines in the woods were able to tell me about some of the things around there, including a really wild local legend about some super rich lady who died with her house girls and buried a golden elephant at some secret place in the woods. Who knows if the legend is true -- its probably just some wild exaggeration across the generations -- but finding a genuine local legend of that sort was itself quite an interesting discovery to me (and a personal triumph of my then-not-so-good Japanese).
Here is a map link to the area (quite a few things seem to be missing, but you can tell its pretty dense even just with active-but-unvisited holy places). The mountains around Nara are loaded with similarly neglected pathways.
Due to the nature of the OP's request there really isn't a way to find these things other than to go look for them.
[As another bizarre side-note to add to the stack of bizarre side-notes that comprise this answer, the Yamaguchi-gumi have a head office there on the ryokan road that descends into Ikoma City. That was quite a surprise. The whole area is so weird, though, that it doesn't stick out as specially weird. Ikoma Mountain is by no means unique in Japan as a place positively overflowing with ancient and modern clashes, and surprises awaiting the observant traveller of the active and forgotten variety from either ancient or modern eras.]
UrBex Japan
and see if you can get in contact with any of these people to get to know the deserted spots. However, keep in mind it can be a closed community and sometimes the UrBexers guard the knowledge of deserted places closely.