The walk from the station to Meiji Shrine is perhaps 20 minutes, but as I recall, it's strictly a footpath. At least I've always walked from Harajuku Station through the park-like area to the shrine. Others who have been there more recently may correct this impression.

Nijo Castle, Kinkakuji, and Sanjuusangendo should all be accessible by taxi, as they are on flat ground, although there is some walking to get from the entrance of Kinkakuji to the actual temple. Kiyomizudera is built into the side of a mountain, and I have always walked up a winding street. I honestly don't remember whether there is motorized access.

I haven't done the fish auction, so I can't comment on taking a taxi from the Keio Plaza to Tsukiji. But the streets should be fairly empty at that hour. The expense (higher fares in the wee hours, since the trains aren't yet running) would be more of a problem than the time.

I wonder if the concierges at the Keio Plaza and your Kyoto hotel could arrange for you to rent a folding wheelchair (having had experience with elderly relatives, I know that there are some fairly lightweight models) for places where walking is unavoidable.