Itinerary & travel options

If you want authentic and less touristy, then go to towns and villages few tourists visit. Every place you mention is a major tourist destination. Alternatives for example, could include Manzanares and Almargo between Madrid and Córdoba, and Jaén between Córdoba and Granada. There’s nothing wrong with visiting major tourist destinations, but since you will have a car, take advantage of the cities, towns, and villages between your main stops.

I will suggest organizing your stops with as little backtracking as possible to save on time spent traveling between places. Your second itinerary seems better at avoiding backtracking.

I started traveling overseas in 1981 when I took a job in Saudi Arabia, since then I have lived in Germany and with retirement now visited 81 foreign countries.

Travel 40 years ago involved fewer tourist and you didn't have to book anything in advance. Now, many Boomers are retired and travel more. Still, despite all the other tourists, I find that the really special places in the World are still wonderful, tourists or not.

The Great Wall of China, Egyptian Pyramids, Parthenon, Sistine Chapel and Tower of London are still must sees.

I do understand what you are looking for in more out of the way places that are not dominated by tourists.
Places like Dinkelsbuhel as walled medieval city, not much different from Rothenberg ob der Tauber in Germany. Both on the Romantic Road and both amazing places, but Dinkelsbuhel has about 5% of the tourists that you find in Rothenberg. Does that make Dinkelsbuhel more authentic, not really, but it is still nice.

One thing about wandering in large European cities on your own, do your research prior to going there, since there are some places in Paris, London, and Athens that you don't want to go, for your personal protection.