Kyoto is a city in Japan.
The easiest way and a great place to hitch is directly from the Service Area "Otsu SA". To get there take the JR line eastwards from Kyoto St to Otsu (two stops, 190 Yen). In Otsu, exit the station at the north exit, turn right and walk until the first crossroads with traffic lights. There turn right again and walk straight for 10 minutes. Before you see the motorway bridge crossing your street theres a mound with stairs that leads up to the motorway (Meishin Expy) and directly to the service area. Maybe you have to climb a little fence to get to the stairs that bring you up to the Service Area, but when I was there, the gate was open. Very great and accessible place! https://goo.gl/maps/ogroO
Alternative: From the main station ask your way to Jonan-Gu-Shrine. It's basically a little west from the main station and then about 2 miles south down one and the same road. Once you get to cross a small canal you can see the ramp on to Meishin Expy, which goes west-east, so from Osaka to Tokyo and on. Best position yourself in front of the McD's just before the bridge to go east to Nagoya/Tokyo. Oh, and of course, learn the Kanji writing of the place you want to go to and make a sign.
West towards Osaka,
Oyamazaki Interchange in the South-West of the city. There's a konbini right before the entrance of the highway. We chose to hitch before the on-ramp, it's not the best spot ever but there's enough space for a car to stop. Actually a car stopped pretty soon after we started here, while we were unlucky at the konbini.
Later in our trip, we met a Japanese guy who specialized in picking up hitchhikers. He's from Kyoto, and he told us he was almost every morning at the Kyoto South Interchange (Kyoto-minami in Japanese) from 9 to 11am, waiting to pick up any potential hitchhiker.
To go west from Otsu SA, just start by following the way described above (in the "going East" section). But once you see the stairs on your right, don't go up there because if you find yourself in the side towards Nagoya and Tokyo you won't be able to make it to the other side. So don't go up the stairs but carry on walking, staying on the right side of the road. Be really careful as you walk in the tunnel because there is no real sidewalk and you're facing the traffic. Once you're out of the tunnel, walk for another 50 meters and you'll see stairs on your right, leading to the Service Area. Here's a picture of the stairs.