Where to stay in Kyoto

My family and I (husband and wife with 7 year old son) will be in Kyoto for the first time in late October. We will be there for 3 days and 2 nights. Which part (neighborhood or district) of Kyoto would be the most strategic place to stay while we're in Kyoto?

We have stayed in Kyoto close to Sanjo station (west side of the river and an other hotel close to Kawaramachi station. We had to change hotels in the middle because we booked late but in the end it was quite perfect.
For us those were very good spots to stay. From Kawaramachi station it was very easy to take the train to Arashiyama. From both hotels we were walking to Gion, Imperial Palace, Nijo castle, Philosofers Path and then taking a taxi back to the hotel. (We like to walk...A LOT.)

Also going to Fushimi Inari was really easy by train but I don't remember anymore how, sorry :(

Very nice restaurants close to the hotels.

If you are intrested in Japanese culture, it might be one way to stay at the old Kyoto house.

http://www.machiya-inn.net/home/english-home.html

Generally, most people stay either near the station or near Sanjo/Shijo.

Both have different advantages/disadvantages. I prefer the latter, as it means that you can easily have a quick detour around Pontocho/Gion in the evening without making a specific point of it.

As a regular visitor to Japan, and Kyoto twice a year, I always try and stay at 'The Park Royal Hotel', it is on Sanjo-dori and perfectly located for walking to Nishiki Market, Gion, Ponttocho? ( excuse spelling!), and all the shopping arcades and many restaurants etc...it is in the middle of the main shopping and entertainment area of Kyoto, about 15 minutes from the Kyoto Station and an 'excellent Hotel'. Always my first preference!.