Travel

I've mainly cycled over there...

..but this is a goodish site..

..and I've got this which gives a fair range of walks - although perhaps a little hut biased (you can camp at the huts).

And a few other links I have used to get info..

This has got some interesting stuff,

www.i-cjw.com

Not that familiar with the Kyoto area as I am Tokyo based, so I can't speak from personal experience. I have the Lonely Planet book recommended by Ed H and it has a section on Kansai. However a quick look through that section only shows 2 multi day hikes, one of which is/was closed due to typhoon damage and the other is partly off limits to women!

Of course, you dont have to stick to the Kyoto/Kansai region - the shinkansen can get you to pretty much any region of Japan within a few hours, though its not that cheap - in fact depending on the distance its about the same price as flying, though somewhat more convenient. In a couple of hours you could get to the popular Japan Alps - in september they should be snow free.

Try hyperdia for public transport route planning

In case you are wondering, Japan uses the normal en417 screw type gas cannisters. You can get them from some DIY store and even some department stores, but obviously a proper outdoors type store will be a better bet. The big Montbell chain has a branch in Kyoto - you can find a list of their stores here. BTW, Montbell stuff is pretty good and hard to find in the UK. Montbell Japan prices are OK, especially the factory outlets, though not as cheap as Montbell US for some strange reason. Generally though, I find that outdoors gear is rather expensive in Japan (however I am out of touch with UK prices).

There's probably not much snow (if any) in September, so I dont know if the snow monkeys will show up -  I think they wander further afield when the weather allows. I have never actually seen any in the wild, but then again nearer tokyo a lot of the larger wildlife has become quite rare.

 The jigokudani monkey park is actually right in the middle of 'mountain country' so from there you have loads of hiking opportunities. You may want to purchase a "bear bell" to keep the bears away while you are walking. I personally find the noise quite irritating and I guess the bears do too, but its definitely much better than getting eaten.

 BTW, some things which spring to mind assuming this is your first visit...

Japan is more cash orientated than the UK - a suprising number of businesses wont accept plastic. ATMs usually charge a fee which increases outside of office hours. Convenience stores which have ATMs are very common in the cities and generally seem to open 24hours, though in small villages you may well be out of luck.

Eating out in japan is much cheaper than the UK - though touristy areas do tend to get inflated prices

Buses and trains are quite good value in the cities, slightly less so out in the countryside, but taxis are pretty expensive everywhere.

Gratuities (tips) are not the custom in Japan.

Talking of customs, you may end up visiting a temple while in kyoto. Just like entering someone house you should take of your shoes before entering. Keeping a hat on seems ok though. Usually there is a gate into the inner compound which has a raised sill. You should step over this not on it (I dont actually know why this is though, other than to protect the wood work?)

Edit:

Hiring a car is quite practical and familiar if you drive in the UK, and many roadsigns are bilingual japanese/english. Driving may be the only way to access some hiking trailheads. Parking is a problem (i.e. expensive) in cities but usually quite ok (often free) in the mountains. Petrol is reasonable if you are used to UK prices. Speed limits (in Km/h) are quite low which makes for relaxing driving when traffic is light. One thing to watch out for is that a green (blue) light for go often (though not always) means go for pedestrians to cross the side road i.e. watch out for crossing pedestrians when turning at any traffic light controlled junction.