I suspect you'll find the transportation time needed to daytrip to a lot of the cities on Carlos's list takes longer than you would think. I don't object to day trips at all; I do not like changing hotels. But, because of the geography and the number of sights on my target list, I've spent the night in all but 3 of those cities; two I haven't visited yet (Vic and Guadalupe); Comillas I did day trip to, from Santander, which is unfortunately one of of Spain's least interesting cities, architecturally.
Valencia has multiple Calatrava buildings. Cuenca is on the AVE line between Valencia and Madrid. I'd rather stop there for one or two nights rather than attempting it on a day trip. In addition to the hanging houses, Cuenca has a couple of small but interesting modern-art museums and an attractive, hilltop historic center. The AVE station is well outside of town, so time must be allowed for getting into town by bus (not sure how often it runs, especially on weekends) or taxi.
Albarracin, as far as I know, is only accessible by bus from Teruel, and the bus arrives late in the day and departs early in the morning, so even spending one night allows precious little time there. Teruel, which has a lot of interesting architecture, is a rather forgotten provincial capital located on a not-heavily-traveled rail line running from Valencia to Zaragoza. I made the mistake of taking an abbreviated day trip to Teruel on my first visit. The town was so attractive I had to go back, upon which occasion I also took the side trip to Albarracin. Unfortunately, I now want to go back to Albarracin and stay two nights rather than one.
You can easily day trip from Tarragona (Roman ruins) to Reus, Gaudi's hometown. There are no Gaudi buildings there, but there are modernista buildings by others, especially by Domènech i Montaner, and the small Gaudi museum is worth a visit.
Oviedo has some very early churches on the outskirts (transportation a bit challenging); I think they're Romanesque.
If you get to Leon, Astorga is a viable day trip. The bishop's palace in Astorga was designed by Gaudi.
Betanzos is an interesting side trip from A Coruna.
There are many more places worth visiting, but I think you'll find you need to cover less than the full length and breadth of Spain, given the time you have available.
From the map Toledo looks like a reasonable day trip from Madrid, and Cordoba from Seville, but those cities have plenty to keep you occupied for long enough to justify at least a 2-night stay--a situation Carlos has indicated via his suggestions for length of stay.
The Ruta del Modernisme website has a lot of information that will be helpful if you're interested in that type of architecture, which is most heavily represented in Barcelona, where the organization is based. Those folks publish a very attractive guidebook that comes with a money-saving discount booklet. The guidebook is very inexpensive but quite heavy.
I hate to tell you this, but based on historical weather statistics, Seville can be expected to be much, much hotter than what you experienced in Sicily. Average high temperatures in Seville vs. Palermo: 9 degrees (F) hotter in June; 11 degrees hotter in July; 9 degrees hotter in August. It will be brutal.
If you want to take a look at actual, day-by-day weather in recent years, you can find that information on the website timeanddate.com:
Seville weather July 2022
You can use the pulldown box just above the graph on the right to change the month and year. Data should be available for about the last ten years. Use the Search box near the top of the webpage to find information for other cities.
