Rent a car, drive in some random direction

instructions unclear, am now drowning in my keicar in the ocean

Counter point: I loved osaka and kyoto, would skip tokyo before them. On kyoto we went up to the main temples using side streets and small foot paths and down on the main road.

We stayed in a regular neighborhood in osaka, drank and had fun on small 5-people bars with the locals and visited the city center occasionally. Made me appreciate the quiet japanese life even in a big city. Very charming city

Go north. Hardly anyone goes to Tohoku and there's so much to see

I would stay near (ish) to Kyoto and just go one day, the National Museum in Kyoto is really good and you can see the rest of what you want to see quite quickly. It is about as commercialized as you can get for a town in Japan, its approaching Disney levels of parody.

Staying further away lowers the cost and as long as its on one of the direct train lines into Kyoto it doesnt take long to get there. There is a lot to do in daily travelable distance in the region that is a better use of your time.

If you look at stuff in Kyoto at 5 am in the morning (or earlier) it is nice and empty.

Source lived in the Region for a year

Oh, and while I'm at it: do not trust any food recommendation written in English. Good or bad.