Something else you might do on your Gothic Quarter day in Barcelona is at least walk past the Palau de la Musica Catalana. It's another stunning modernista building, but by an architect not named "Gaudi". There are English-language tours offered of the interior, but you will already be seeing La Sagrada Familia and Casa Vicens.
Speaking of which: I am nuts about modernista architecture. I've seen a great deal of it, not just in Barcelona. I was a bit disappointed by the interior of Casa Vicens. It seemed much less interesting to me than Casa Mila/La Pedrera and Casa Batllo. The exterior of Casa Vicens is very eye-catching, but at the time of my 2019 visit, the interior was underwhelming. Perhaps they've done additional restoration work since then. If they haven't augmented what you can see, I wouldn't recommend Casa Vicens to someone with just a few days in Barcelona. Now, the walk from that area back down to the center of the city is a different matter; it takes you through an attractive, relatively non-touristy part of town.
I really liked the tour of the Gothic Quarter offered by the tourist office back in 2016. The tour groups were smaller than the so-called "free tour" groups (for which you must tip generously, because the guide has to pay the tour company several euros for each tour participant). I trust tours offered by tourist offices more, because those guides are paid outright; I count on them to provide accurate information rather than possibly spinning tall tales to try to generate better tips.
I also liked the tour of Madrid's historic center offered by the tourist office in that city.
I am not a shopper. You'll probably see a lot of interesting things in the normal course of your sightseeing. I'd think the larger cities (meaning not Toledo) would offer more options. There's a large department store, El Corte Ingles, right on Placa de Catalunya in Barcelona. That might be a decent place to try if you're in the area. The Barri Gotic probably has more quirky stuff.
Sightseeing tickets to purchase ahead of time--more because the ticket lines can be more than an hour long than because things are likely to totally sell out way ahead of time:
Barcelona: Buy your tickets for La Sagrada Familia and Parc Guell before arriving in Barcelona. The tourist office's walking tour has a limited capacity. The English tours of the Palau de la Musica Catalana can sell out. I haven't heard that Casa Vicens is an issue at all. Casa Mila and Casa Batllo most definitely are. All the tickets I've mentioned are timed, by the way, which is a pain in the patootie. At some places you may be held at the door beyond your ticketed entry time as the door-minder waits for some people to leave. Don't forget to also allow for travel time from place and for meal breaks.
Madrid: You might run into a line-up at the ticket window for the Royal Palace or the Prado. The Royal Palace in particular seemed to me very popular with out-of-town Spaniards. It might be busier than average on holidays and weekends.
Seville: Lines for both the Alcazar and the Cathedral are very long, outdoors and uncovered. At the time of your trip Seville may very well see temperatures over 100F. You don't want to be standing out in the sun on days like that. You can get those tickets online. I know the Alcazar ticket is timed; I'm not sure about the Cathedral ticket.
Toledo: I think the busiest sight in Toledo is the Cathedral. I happened to run into a bit of a line there, but it was a religious-holiday weekend. That may have been unusual.
Keep in mind:
Spain eats late. Lunch--usually the big meal of the day--is about 2 PM to 4 PM. Dinner is equally late.
Barcelona has perhaps the world's most skilled pickpockets. Protect your valuables, including your smartphones. Be careful in at all your destinations, but especially so in Barcelona along the Ramblas and in the Gothic Quarter.
