Congrats on making the move. Holy moly did you dodge a bullet in LA!

I've lived in a few old cities in Europe, and vicariously in quite a few more through my wife and close friends. In Vienna I've lived in 6 different apartments for 3 or more years all over the city (including inside what used to be the old walled center).

If possible I'd try to rent a place for 3 years (or whatever short term rental contracts are in Valencia) near stuff you and your wife really like to do now. That will give you time to get to learn the city.

I expect very much that after 3 years of being "residents with mostly tourist eyes" you'll have a better idea of what parts of the city more fit your tastes (and there may be multiple).

IMO infrastructure (groceries, drug store, cobbler, etc.) and multiple public transport modalities make for the best long-term place to live, balanced against price.

Check out working districts that allow you to get around town quickly, but where you can get a place 2x the size or 2x nicer than a place 5 minutes away on the subway or 10 minutes by streetcar.

Keep in mind it is an old European city and if you want or need to, you can always walk (especially in a climate like Valencia). Things are not that far away as how they look on a map.

I get the grid thing. I'm an engineer. I think you'll find that part of the charm of living off the grid (see what I did there?) is really easy once you've lived there a while.

IMO you get a more personal feeling when you connect a destination with districts and then landmarks than with street names and a grid. Your mileage may vary.