Itinerary Suggestions

You could go see the exterior of the Palau de la Musica Catalana on Day 1.

If you haven't already done so, you should buy tickets to the following sights before arrival in Barcelona to avoid long lines and possible sell-outs: Picasso Museum (Severe crowding alert! Not worth it if you're not a big fan), Casa Mila, La Sagrada Familia, Parc Guell.

Thank you!
I will look into that for sure. I will be buying tickets tonight for the sights. I am still unsure about the museum as I hade read a lot about overcrowding.

Barcelona has a lot of other art museum that are much more pleasant to visit than the Picasso. If you like Miro, that museum is highly recommended. But it is a single-artist museum except for any special temporary exhibition that might be running.

The Museu Nacional d'Art de Catalunya is very good. It's on Montjuic. It would be a push to try to see the whole thing on Day 3, because it's large, and I know a lot of people can't take more than 2 hours of an art museum at a time. But you could choose a few sections to visit. The MNAC has a couple of especially interesting/unusual collections. The modernism collection focuses on decorative art, furniture and jewelry. Then there are the fabulous medieval frescoes rescued from churches in the Pyrenees. I'm not a particular fan of church frescoes, but this is a great opportunity to see some impressive ones. I'm not sure there's a better place to see such things anywhere.

Have you checked "Devour Madrid", or "Devour Seville" website? The have some lists of preferred restaurants.
They also have food tours, but you do not have to book one to get the info.

I have no financial interest in the site, I just watched some of their youtube vids, and they have great information.

Have fun!
Marie

Day 1 is very light. Day 2 is too much. I'd expect a walking tour of the Gothic quarter to include the cathedral. If you want to have lunch at La Boqueria (touristy), it's a lot closer to the cathedral than Casa Batllo.

The Picasso Museum is for fans. It doesn't have any major works or any works for some of his well-known periods. It shows more his development in his early teens and his cubist period. It's usually very crowded. Seconding, acraven's suggestions, it's a pleasant downhill walk on Montjuic from the Miro to the MNAC, if you leave the road and walk through the gardens there are some good views of the city below. MNAC has a good, reasonably priced cafe.

We did a great tour with Barcelona Day Tours that included all the Gaudi sites that you mentioned. Only thing, we didn't go in Sagrada Familia, had to go back for that. Consider a tour, you will save time.

Tickets to Parc Guell now include a free shuttle-bus ride from one of the Metro stations, so I'm not sure a bus (?) tour that got a traveler into Parc Guell and Casa Mila would be a time-saver.