October 2009 update: Sadly Shougetsu-An has now closed. However, further up the street (towards Sanjo) you can find its sister restaurant Shiki-Yoshina. It also has a yuka balcony in the summer season and a very similar menu. Another branch of the same group is the restaurant Hamacho just north of Sanjo on Kiyamachi, however this restaurant does not have a riverside balcony.
A year ago I wrote about dining on the yuka balcony of Pontocho retsaurant Shougetsu-an. Last night I celebrated my birthday there and it was so nice! Wonderful food, great service and situated half-way twixt Shijo and Sanjo we had a wonderful twilight view over the Kamo river. 
Unfortunately, I’ve learned that Shougetsu-an is moving next October to Gion, so this summer is your last chance to enjoy yuka dining there.
Here are some pictures for you. This is the tempura:
This the sashimi:
This, myself and Mewby having a lovely time:
Really, one thing anyone visiting Kyoto must try during their stay is a balcony dinner over-looking the Kamo river and I really recommend this restaurant. 
The food (beautifully presented!) is top-notch but the service is excellent too and the staff really make an effort to make your evening a happy one. They have English menus if required and can also arrange for a special set course if you have particular dietary requirements. Shougetsu-an is almost exactly halfway between Sanjo and Shijo on the east side of Pontocho, on the corner by the park. Check out this website for details. There is a map up here. 17:00～23:00 (Last Orders: 22:30)
Tel: 075-223-1401
Took your advice and visited here. As we had walked into the alley from the opposite end (towards the south), we got to go through the entire area before finding the restaurant. It’s too bad we didn’t get to sit outside, but it started to pour, so no complaints. 😛
Was a great dinner.
Glad you liked it. Sadly Shougetsu-an has now closed. I believe a new restaurant will be opening up on the same premises but I haven’t checked it out yet. I must update the article!