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