Below are a few possibilities around JR Kyoto station. (If you like shopping, you might want to explore the hotels in Kawaramachi/Karasuma area, below.)

Some reference points:
★★★: most expensive
★★: relatively less expensive
★: least expensive

Hotel Kanra Kyoto★★★
http://www.hotelkanra.jp/en/index.html
http://www.hotelkanra.jp/

Hotel Anteroom Kyoto★★★
http://hotel-anteroom.com/

Monbou Kaikan★★★
http://monbou.jp/index_e.shtml
http://monbou.jp/

Hotel Granvia Kyoto★★★
http://www.granviakyoto.com/
http://www.granvia-kyoto.co.jp/index.html

Rihga Royal Hotel Kyoto★★★
http://www.rihga-kyoto.co.jp/index.htm

Dormy Inn Premium Kyoto Ekimae★★★
http://www.japanican.com/hotels/shisetsudetail.aspx?st=6231A11&ref=dormy
http://www.hotespa.net/hotels/kyoto/?gclid=CL3WosXhm6oCFahLpgodqypExA

New Miyako Hotel★★
http://www.miyakohotels.ne.jp/newmiyako/english/index.html
http://www.miyakohotels.ne.jp/newmiyako/index.html/

Daiwa Roynet Hotel Kyoto-hachijoguchi★★
http://www.daiwaroynet.jp/kyoto-hachi/

Kyoto Century Hotel★★
http://www.kyoto-centuryhotel.co.jp/english/index.html
http://www.kyoto-centuryhotel.co.jp/cgi-bin/cms/index.cgi

Kyoto Tokyu Hotel★★
http://www.kyoto-h.tokyuhotels.co.jp/en/
http://www.kyoto-h.tokyuhotels.co.jp/

Hotel Hokke Club Kyoto★★
http://www.hokke.co.jp/2601/

Kyoto Tower Hotel★★
http://www.kyoto-tower.co.jp/tower_hotel/english.html
http://www.kyoto-tower.co.jp/tower_hotel/

Apa Hotel Kyoto-ekimae★★
http://www.apahotel.com/hotel/kansai/01_kyoto-ekimae/english/index.html
http://www.apahotel.com/hotel/kansai/01_kyoto-ekimae/index.html

Hotel New Hankyu Kyoto★★
http://www.hankyu-hotel.com/cgi-bin2/cms2/index_en.cgi?hid=30kyotoshh
http://www.hankyu-hotel.com/hotel/kyotoshh/index.html

Apa Villa Hotel Kyoto-ekimae★★
http://www.apahotel.com/hotel/kansai/02v_kyoto-ekimae/english/index.html
http://www.apahotel.com/hotel/kansai/02v_kyoto-ekimae/index.html

Kyoto Daini Tower Hotel★★
http://www.kyoto-tower.co.jp/daini_tower_hotel/english.html
http://www.kyoto-tower.co.jp/daini_tower_hotel/

Urban Hotel Kyoto★★
http://uh-urban.com/kyoto/contents/english/index.html
http://uh-urban.com/kyoto/index.html

Kyoto Daiichi Hotel★★
http://www.kyoto-1-hotel.jp/english/index.html
http://www.kyoto-1-hotel.jp/index.html

Kyoto Plaza Hotel★★
http://www.kyoto-plazahotel.co.jp/

Super Hotel Kyoto Karasuma-gojo★
http://www.superhotel.co.jp/s_hotels/karasuma/karasuma.html

K's House Kyoto★
http://kshouse.jp/kyoto-j/

Below are a few possibilities around Hankyu Kawaramachi/Karasuma station. This area is the centre of downtown Kyoto. If you're fond of shopping, you might find the area amusing.

Some reference points:
★★★: most expensive
★★: relatively less expensive
★: least expensive

Kyoto Hotel Okura★★★
http://okura.kyotohotel.co.jp/english/
http://okura.kyotohotel.co.jp/

Kyoto Brighton Hotel★★★
http://www.brightonhotels.co.jp/kyoto/en/index.html/
http://www.brightonhotels.co.jp/kyoto/

Hotel Nikko Princess Kyoto★★★
http://www.princess-kyoto.co.jp/english/index.html
http://www.princess-kyoto.co.jp/index.html

Mitsui Garden Hotel Kyoto Shijo★★★
http://www.gardenhotels.co.jp/eng/kyoto/
http://www.gardenhotels.co.jp/kyoto/

Hotel Monterey Kyoto★★★
http://www.hotelmonterey.co.jp/en/htl/kyoto/index.html
http://www.hotelmonterey.co.jp/cgi-bin/portal/cms/hotelindex.cgi?hid=monkyo

Village Kyoto★★★
http://hotel-village.jp/kyoto/eng/
http://hotel-village.jp/kyoto/

ANA hotel Kyoto★★★
http://www.ichotelsgroup.com/h/d/6c/1/en/hd/kstna
http://www.ana-hkyoto.com/

KKR Kyoto Kuniso★★★
http://www.kuniso.com/

Rhino Hotel Kyoto★★★
http://www.rhino.co.jp/english/index.html
http://www.rhino.co.jp/

Karasuma Kyoto hotel★★★
http://karasuma.kyotohotel.co.jp/english/
http://karasuma.kyotohotel.co.jp/

Hotel Harvest Kyoto★★★
http://www.resorthotels109.com/en/kyoto/
http://www.resorthotels109.com/kyoto/

Royal Park Hotel The Kyoto★★★
http://www.rph-the.co.jp/kyoto/

Kyoto Garden Palace★★★
http://www.hotelgp-kyoto.com/english1
http://www.hotelgp-kyoto.com/

Hotel Toyoko Inn Kyoto Shijo Karasuma★★
http://www.toyoko-inn.com/eng/index.html
http://www.toyoko-inn.com/

The palace side hotel★★
http://www.palacesidehotel.co.jp/english_site/
http://palacesidehotel.co.jp/

Hotel Mystays Kyoto Shijo★★
http://www.mystays.jp/location/ms_kyotoshijo/

Best Western Hotel Kyoto★★
http://www.bwjapan.co.jp/kyoto/en/index.html
http://www.bwjapan.co.jp/kyoto/index.html

Kyoto Kokusai Hotel★★
http://www.kyoto-kokusai.com/e/index.html
http://www.kyoto-kokusai.com/index.html

Kyoto Kokusai Hotel★★
http://www.kyoto-kokusai.com/e/index.html
http://www.kyoto-kokusai.com/index.html

Mitsui Garden Hotel Kyoto Sanjo★★
http://www.gardenhotels.co.jp/eng/sanjo/
http://www.gardenhotels.co.jp/sanjo/

Hotel Unizo Kyoto★★
http://www.hotelunizo.com/eng/kyoto/index.html
http://www.hotelunizo.com/kyoto/index.php

Hotel Oaks Kyoto Shijo★★
http://www.h-oaks.co.jp/kyoto-shijo/english/index.html
http://www.h-oaks.co.jp/kyoto-shijo/index.html

Ark Hotel Kyoto★★
http://kyoto.ark-hotel.co.jp/index.html

Viainn Kyoto Shijo-muromachi★★
http://kyoto.viainn.com/

Kyoto Central Inn★★
http://www.kyoto-centralinn.jp/

Kyoto Horikawa Inn★★
http://www.horikawa-inn.com/

Kyoto City Hotel★★
http://www.kyotocity-hotel.com/index_E.html
http://www.kyotocity-hotel.com/index.html

Hotel Sunroute Kyoto★
http://www.hotel-sunroute-kyoto.co.jp/

Super Hotel Kyoto Shijo-kawaramachi★
http://www.superhotel.co.jp/s_hotels/shijyo/

Hotel Gimmond Kyoto★
http://www.gimmond.co.jp/kyoto/english/e_index.html
http://www.gimmond.co.jp/kyoto/index.html

Court Hotel Kyoto Shijo★
http://www.courthotels.co.jp/kyoto/

City Pension Le Liond'or★
http://www.leliondor.jp/

Hotel Alpha Kyoto★
http://www.japanican.com/hotels/shisetsudetail.aspx?st=6230028&ty=rsv
http://www.alphakyoto.com/

Kyoto Rich Hotel★
http://www.rich-hotels.co.jp/kyoto/

For more possibilities, the following search links would be useful if you're familiar with Japanese websites:
Jalan
Rakuten Travel
Ikyu.com