One of our local joints - *Rive Gauche - is a lovely little bistro on Nijo dori (st) just east of Kawabata Dori (on the south side of the street). One talented chef, one charming waitperson/host/sommelier, good french food (with Japanese influence), small but interesting wine list and decent prices. Dinner including wine costs between 3500 to 8000 yen per person depending on the 'set' or course that you choose so its erring on the more exxy side of things if you are on a budget but the lunchtime deal of soup, main, bread, dessert and coffee/tea for 1500 yen is a steal.
Its a tiny place, not unusual in Japan, which provides and instantly intimate atmosphere -perfect for a romantic dinner or a sole diner looking for a quite place to enjoy a good meal.
Check it out if you are in the Heian Jingu area and walking back towards the city along Nijo dori post morning sightseeing - worth knowing about for an elegant lunch that won't break the bank.
*don't forget to use Google chrome for instant translation of the Japanese website.
And we are talking very good quality everything from housemade mini epi loaves and good butter to fine tea/coffee and petits fours.
I highly recommend the horohoro - guinea fowl (above which seems to be a speciality of theirs.