If you're in the Kyoto area, it's well worth the short train journey to Arashiyama. Using your JR Rail Pass, it's about 15 minutes from Kyoto arriving in to Saga-Arashiyama Station on the Sagano Line. We stayed in central Kyoto near Karasuma so it was a quick trip on the Tozai line to Nijo Station and then the Sagano line to Saga-Arashiyama, about 25 minutes total.
Arashiyama is a fairly touristy area and can get quite busy. However, there are a few reasons that make the trip worthwhile.
Probably most famous of all the attractions in Arashiyama is the Bamboo grove. I was a little surprised when I arrived at the bamboo grove (less than a ten minute walk from the station that's well signposted). Most of the photos you see show the grove as a relatively calm, quiet place. This does not match my experience. Despite the photos, it was really busy. Whilst I'd heard this might be the case, I wasn't expecting there to be taxis driving along the road you're on as you walk through the grove. The further you walk though, in general, the quieter it gets.
Do make sure you walk right to the end though, not least because it's the entry to the next attraction.
Okochi Sanso (Ōkōchi Sansō) Villa & Gardens
This is one of the more overlooked gems in Arashiyama, and was relatively quiet on the day we visited (I suspect because of the roughly 1000 yen entry fee). Okochi Sanso Villa is a collection of buildings and gardens originally built over a number of years by famous Japanese actor Okochi Denjiro. The buildings aren't accessible but the gardens are worth the entry price alone. Especially in autumn, which is when we visited.
The gardens are separated in to different types of arrangements, including moss gardens, trees, shrines and a tea garden (the entry fee includes a cup of tea). What's impressive is how the paths are crafted to reveal different parts of the gardens to visitors.
It isn't all about the gardens though. As you meander your way through the property you are, at various points, presented with wonderful views of Kyoto. Again, stunning in the autumn when the colours are out.
Iwatayama Monkey Park
Visiting the monkey park is not for the faint of heart. The visitor centre is approximately 160m up (as in 160m up, you'll be walking further) a steep, twisting path that has to be walked (there's no other way up). On a hot day, it's quite a challenge. Depending on your fitness level and the weather, you're looking at a hike of between 20 and 45 minutes. There are two routes, one of which is steeper but shorter, and another which is longer but less steep.
As you can see from some of these images, the path isn't necessarily well maintained either. In some parts it's quite overgrown and most of it is uneven. You're fortunate if you're walking on a section with a handrail (although most of the really steep sections do have handrails). There are some wonderful views of Kyoto though.
It's also important to manage your expectations when arriving at the park itself. The visitor centre is little more than a shed with a small shop and toilets. You can purchase food to feed the monkeys for around 100 yen, but you have to feed them from within the building, you are not permitted to take the food outside with you. These are wild animals after all, and I can imagine it being quite uncomfortable were they to round on someone they believed to be carrying food. There are warning posted around the area to this effect advising you to avoid eye contact (although I don't know what "Don't put a load on outside" means!). I did receive a warning from one of the monkeys who gently punched me on the leg, but I'm unsure what my indiscretion was!
What's remarkable about the Monkey Park is that there are monkeys everywhere. You have to be careful walking around so as to not step on one. Even when you're walking up to the park (and back down again) there are monkeys in the trees above you. You can hear them, and see them. It really does feel rather wild at times. There are regular feedings performed by the staff in the park which brings out even more monkeys that were previously hiding in the trees.
Thankfully the walk down is much easier. If you're a fan of wildlife (I'm told there are rare birds in the area as well), it's a worthwhile visit.