If you are looking for an cosy spot for a bowl of pasta in Kyoto's Heian Shrine vicinity head to 'Ogino' on Nijo Dori. It's only about a 5 minute walk west from the corner of Jingu michi (which is a block south from the shrine's entrance).
Their Carbonara and Amatriciana, whilst not completely authentic are really delicious, they also do excellent grilled local meats - the pork is sensational. And the chef/owner is a real sweetie with a penchant for dancehall, ska and reggae - particularly The Whaling Whalers - all on vinyl. There is a small but decent by the glass wine selection. And a couple of desserts.
When I say cosy, I mean real cosy - there is this one area at the front which seats upto 6 then 2 tables for 2 in front of the counter which also seats about 3 people. Still it's bigger than some Japanese restaurants! I'm just saying - go solo, take a friend or go in a very small group. In the evenings it is a nice casual spot for couples. We lived about 10 meters away for 6 months and we were regulars - sure it was convenient but the food was really good and at the right price.