I like Tandir Kebap (slow roasted lamb - oddly similar to an American Boston butt roast) so I asked a native what his favorite Tandir place was and he recommended Haci Sukru. I have been there twice and it has been great both times. I will warn you that it is a lunch place and not a dinner place. Tandir waits for no one and when it's gone they close the restaurant. I went at 11:30AM the first time and 2:30PM the second time and it was good both times.
There is no parking to speak of. I have had luck parking around the corner and walking back. Staff (as usual at a Turkish restaurant) is very friendly and helpful.
Kaynak: http://www.tripadvisor.co.uk/Restaurant_Review-g298014-d1494190-Reviews-Haci_Sukru-Konya.html