Kyoto Accommodation - Modern Ryokans/Inns

Ryokan Shimizu (ranked no.1 on TripAdvisor's list of Kyoto inns). See Tripadvisor user reviews. JapaneseGuestHouse user reviews. Glowing reviews! All 12 rooms with private shower/Western toilet! Small but clean and comfy. Excellent service. Only ¥5250 (S$66) per person - high season surcharge may apply in autumn). Located 7-10mins from Kyoto Station. Book early! More photos from japaneseguesthouse.com (they also feature photos taken by guests)
644 Kagiya-cho, Shichijo-dori Wakamiya Agaru, Shimogyo-ku, Kyoto 600-8317

Kikokuso
Only three rooms in this cosy, richly atmospheric wooden ryokan. Cross the red taikobashi bridge and come to your room. Only one room has private bath. Pet dog Gonta is a cutie (omg he has been featured in magazines!). Rates from ¥8,000 to ¥30,000 (with dinner & breakfast), I think. 5 min taxi from JR Kyoto Station. More photos from a traveler here.

Heianbo
Ranks no.8 on TripAdvisor - read reviews. Just 3 min walk from Kyoto Station. "The futons were super comfortable, the room was super clean and the slippers are bright green." Rooms with bath, no meals ¥6,300 (S$80) per person. Japaneseguesthouse reviews. Hmm not THAT cheap if you compare it to the Budget Inn or Shimizu.
725 Heian-cho, JR Kyoto-ekimae, Shimogyo-ku, Kyoto 600-8216

Ohanabo looks pretty good too, but is more expensive than most budget ryokans. Rooms with baths available too. It's opposite the Higashi (East) Honganji Temple, and 5 mins walk from Kyoto Station. Multicourse dinner available for 5,000 yen. English page with more photos here. Twin rooms ¥14,700 (S$185) and triple rooms ¥20,475 (S$256). And they charge ¥1,575 for babies up to one year old. Photos from a traveler here. 66-2 shokuya-cho, Shimo Juzuyamachi Agaru, Akezu Dori, Shimogyo-ku, Kyoto 600-8158

Hatoya Zuihoukaku is also recommended. Room rate per night with breakfast is ¥7,000 per adult. Also five mins from Kyoto Station Karasuma exit.

Ryokan Yuhara - gaijin-friendly small ryokan also very warmly raved about. Oops no bath attached.

Keep these links handy:
Welcome Inn Reservation Centre
TripAdvisor ranking of 41 B&Bs/Inns in Kyoto
Japan Ryokan Association listing

There is an interesting alternative - VBRO - Vacation Rental By Owner - short stay rentals in one-two bedroom choices ranging from a traditional home, townhouse or modern apartment. There's even a studio apartment furnished with Muji accessories! Most require minimum 7-day stay though.