The Sagano Romantic Train is a fun excursion from Arashiyama. It follows an old train route along the gorge of the the river that goes through Arashiyama. The train is an open-air train, with really picturesque views. Just a warning, though, the train is rather loud, so you might want to bring earplugs. The best views seemed to be on the right side of the train, when going from Arashiyama to Sagano. You can buy a raft ticket at the train station and raft back down, which looked like a lot of fun, which gorgeous views (heh, quite literally). Unfortunately, I was short on cash, so wasn’t able to do it. If you opt to take the train back down, you basically just stay on the train, or get off and get right back on. I had a misunderstanding where I thought I need to walk a few minutes to the next train station, so I missed the train back down. But if that happens, there is a JR station 5 minutes away, and you can take the opportunity to go to the Byoudou-in temple in Uji (transfer at Kyoto station).
I definitely recommend the trip, particularly if there is a romantic interest with you (in which case, do the raft, too). You can get to the train station by going through the bamboo path
and turning right at the end.