So if Sevilla is a mess on Holy Thursday, opt for Zaragosa (easily reached by fast train from Madrid) or Valldolid. Both are famous, in Spain, for their big processions. I spent one Holy Thursday in Zaragosa and it's certainly in the top ten experiences of my life. I booked on my way to town, so no trouble finding lodging. There are crowds but few tourists and 26 processions that begin Thursday afternoon and continue to almost dawn.
In general, I think the first decision is whether to stay north or go south. If you go south, you can do a loop that includes Cordoba, Sevilla and Granada. You don't have a lot of time so probably not too much beyond that. Cordoba has an amazing mosque turned cathedral and surrounding medieval quarter. Sevilla has one of the best alcazars and Christopher Columbus' bones are in the cathedral (plus a famous Semana Santa), Grenada has the Alhambra and very interesting medieval center.
If you stay north, you can get to Toledo easily by train and walk from there. It's my favorite medieval center in Spain. I'd suggest a loop by car than includes: Avila, Salamanca, Zamora, Valladolid, and Segovia. Avila's wall is dramatic, Salamanca has one of the best cathedrals, Zamora has a surprising amount of historical sights, Vallodolid has a long list of sights plus Semana Santa, Segovia is a rare place where a castle, medieval center and old aquaduct are all within walking distance. There's also a circa 600 AD Templar style church just outside of town. It's not big or heavily decorated but it's a good representation of a church from that time. There are also three big castles in Valladolid area, Coca, Penafiel, and la Mota - any or all would be worth a visit. Admission to Penafiel includes admission to the wine museum in town, you may be able to kill two birds with one stone. Most of the bodegas in the country don't have drop-in wine tasting (Jerez' sherry producers are the big exception), a reasonable substitute is a local wine museum. They're typically housed in an old bodega and I think all have a wine bar serving local wines.
Madrid, IMO, has few sights past El Prado (a world class gallery). There are a lot of special interest museums but they pale in comparison to seeing other Spanish cities. Madrid is roughly the age of Baltimore, very new by European standards - which leaves it with no medieval center. I did enjoy the Temple Debod, which was donated by Egypt to thank the Spanish for help with the Aswan Dam.
Madrid and Barcelona are fairly infamous for theft, so keep track of your valuables there. You might run into it in Seville during Semana Santa since thieves follow tourists.
I like Barcelona a lot. Don't plan it during Semana Santa unless you specifically want to avoid celebrations. The only sign of Holy Week in Barcelona is added masses in the churches. Barcelona is the least religious city in the least religious area of Spain. There is one procession on Good Friday that was started by Sevilla expats, just so there would be something, but it's not connected with the local church.
George Orwell's book Homage to Catalonia is a good read if you want to know more about the politics and history related to the Spanish Civil War.