An active day, biking to Kurama 鞍馬 valley to soak in the onsen 温泉 (hot spring bath).
Rent bicycles. Some of the rental places can seem slightly sketch, but they're not. The prices are fair. The worst thing you might find is that no one is tending the shop for half an hour chunks at a time. Beware that you might need to budget some time for rental and return, especially if you don't speak Japanese.
The ride to Kurama is uphill the whole way, and so arduous. Yet, it's really pleasant nonetheless. You do not have to ride on streets very much: You can start by riding north along the east bank of Kamo-gawa, the river that runs North-South through the city. Then, the river splits into two rivers (actually, two rivers join to become Kamo-gawa) at Demachiyangi-station. The bicycle ride is about 1.5 hours from there. You can actually trace either river to make your way toward Kurama valley. Keep your eyes out for signs to Kurama.
[Note: If you don't want to bike, you can take the Eizan electric railway Kurama line from Demachiyanagi-station.]
There are a couple of things to see along on the way. One is a very famous Japanese sweets shop called Demachi Futuba 出町ふたば just a few blocks west of the river split (at the corner of Kawara-machi 河原町 and Imadegawa 今出川). I don't care how long the line is -- wait it out, and buy their mame-mochi (white mochi with dark adzuki beans barely visible from under the surface)! I also recommend their warabi-mochi (made from fern-bracken). Even a long looking line shouldn't take long.
Also near the river split is Shimogamo-Jinja, an important Shinto shrine with lots of tree-lined paths. If you take the river that goes northwest from the split, you can check out its sister shrine, Kamigamo-Jinja. These are some of the best Shinto shrines Kyoto has to offer, and the latter is kind of a hassle to get to without bikes.
That's a reason to bike, but why else? Well, it's lovely to get exposed to the Kyoto suburbs from the river. It is also amazing to take a long bath at Kurama onsen after the exercising! But the best part is getting to cruise all the way downhill into town after refreshing yourself...like an hour with almost no peddling. So triumphant!
Once you get into Kurama valley there are some awesome destinations. Kurama temple is glorious. It's very vertical, and has an extremely lovely view from the top.
Near the entrance to the temple is one of Kyoto's best restaurants! It's called Yōshūji, and it serves vegetarian/Buddhist cuisine. Get the most expensive set menu (aprox. 3000¥). It's filling and absolutely worth it.
Finally, bathe at Kurama onsen, a true outdoor mountain hot spring with stunning views of thickly growing pines on the opposing mountainside. The view is especially nice when wisteria is in bloom. There are two rotating gender-separated baths. A basic bath set will run you in the ballpark of 1000¥.
You'll be tired from the physical activity and bathing, so plan for nothing else that day. You don't have to start all that early, if you rent bikes the day before, and are happy to keep them the for the following day. Many bike rentals close at 5, so an early start is needed if you only want to rent them for the day.