I stayed in Kyoto from Nov 11 thru the 15th this year and this was my booking experience: Prior to June, there was very little availability; most of the available hotels were in either the Kyoto Station or Shijo/Karasuma areas. I made a couple of back up bookings just in case. By the 3rd week of June there were many hotels available so I booked a hotel in the Sanjo Kawaramachi area which was my preference. Out of curiosity I checked again about 2 months out, and while there was quite a bit of availability for my dates, there was almost nothing from the 15th onwards (I book my hotels thru Rakuten Travel btw).

There are many inexpensive business hotels near Kyoto Station such at the Hankyu, Kyoto Tower, and APA Hotel. For something a little bit different you might try the Hotel Station Kyoto http://www.hotel-st-kyoto.com/eng/west_top.html, I booked it for some friends once and they thought it was pretty nice.