The site for the USA Embassy is a good website.  If you scroll down to Tokyo and Kyoto it offers a number of cities and hospitals.

However, the best advice is probably to take some contact details with you, however enquire at the hotel and ask that they make phone enquiries with the closest hospital on your behalf.

Medical Resources in Japan by the USA Embassy:

http://japan.usembassy.gov/e/acs/tacs-7119.html

 

The Australian Embassy site in Japan:

http://www.australia.or.jp/en/consular/emergency/#services 

You can also reach many medical information sites from the following:

http://au.search.yahoo.com/search?p=tokyo+medical+emergency&toggle=1&co                                                                              

Japan National Tourism Organisation - Guide for when you are feeling ill:

http://www.jnto.go.jp/eng/arrange/essential/emergency/mi_guide.html

Japan National Tourism Organisation - If you become ill:

http://www.jnto.go.jp/eng/arrange/essential/emergency/ill.html

Japan National Tourism Organisation - Guidebook for when you are feeling ill:

https://www.jnto.go.jp/eng/arrange/essential/emergency/pdf/guide_eng.pdf

The Expat's Guide to Japan - List of English speaking hospitals and clinics in Tokyo:

http://expatsguide.jp/health-safety/medical-care/hospitals-clinics-tokyo/