Sundays in Barcelona

We went to the Picasso museum on Sunday mid day. The line seemed long but moves fast.

I don't know how crowded it is on free Sunday, but the National Museum of Catalunya is huge, so I imagine it could absorb crowds better than the smaller and more famous Picasso Museum. It's also highly worthwhile. Regular tickets are good for two days within a 30 day period; I wish I could have spread my visit over two days, as I could only see less than half of it despite spending several hours there. If you like Modernista furniture, it's a must. http://www.museunacional.cat/en/at-a-glance

La Boqueria, while fun, is not the only thing to see in the Gothic Quarter; I wouldn't skip that tour just for this reason. You can always return to La Boqueria, or any other market, on another day when they are open.

Sunday would also be a good day for a walk around the Eixample looking at Modernista architecture, and (with pre-booked tickets) going inside some of the houses. Or to go to Barcelonetta near the water. Or up to Tibidabo or Montjuic for the views.

Picasso Museum opens from 9am. This time is VERY early for the locals, especially on a Sunday. I would get there at opening and you should be fine. Visit Basilica Santa Maria del Mar afterwards, then book the 13:00 tour at Palau de la Musica Catalana before walking Passeig de Gracia from Placa Catalunya to Diagonal. Save the Ramblas and La Boqueria for Monday.

... it's not that's "very early"... it's that our Sundays work differently than yours :))

You will wake up later than normal, 9ish (even 10ish), you will have a coffee either at home or at the corner coffee shop while reading the paper, then a stroll either in the neighbourhood with the dog or the kids (if you have them), or to one of the parks in the city, or downtown to Barri Gòtic, or by the promenade by the beach, or simply sitting on a terrace having a beer and people watching (that's sort of a national sport here in Catalonia), then fer el pica-pica (of course, that's quintessential!), then most likely heading home for lunch (or simply staying in the area and lunch in your preferred restaurant)... AND THEN it's time to visit a museum -moreover taking into account many are free from 3pm onward- or going to the cinema or meeting with friends (occasionally with the family too) to spend the afternoon/evening. There are of course variations but this is a pretty good description of a typical Sunday for many Barcelonians.

As a general rule, time is valuable so it can be a better value to pay admission and visit on a slower day than take advantage of free admission. I ran into that at El Prado. We arrived maybe 20 minutes before free admission began. The line outside looked like they were waiting for a Rolling Stones concert, not only long but five or more across. Inside wasn't bad, but it would probably have been worth it to visit three hours earlier and spend the time viewing art rather than spending a significant part of the free admission time waiting to get through the line.

It depends on the weather and what you would like to do. Early in the morning you will be able to quickly enter the museums (most of them may be closed on Mondays).

I would book in advance including the audioguide for Picasso and Miro, which is up in Montjuic and will offer you a great place to walk around with a beautifull view of the city.
You could go to Barcelonetta and the beach, or climb up to Tibidabo.

On Sundays in Placa St Jaume it is possible to visit the townhall between 10 and 13:30 and this is close to the Picasso museum. Nearby is the Mercat de Santa Caterina which is closed on Sundays but at its entrance we ate in an original tapas bar/restaurant
I love the Old City and everything right and left of Ramblas, it's just that most shops are closed and without them it's not the same to stroll the narrow streets and get lost in the shops