First, Enric you are a gem and I will be writing down all your hints/comments.
We are planning this trip for end of June/early July next year and have not decided how many days in Barcelona and surroundings. We may never get back to Barcelona, so we want to do it well this time. So how many days should we plan, also must take a good bit of the heat of the day off. We can't do but one museum a day (1/2 day) too much stimulation. Montserrat is a must and we don't want to rush this. We also plan on a food/wine tour of Barcelona.
How interested are you in the modernist architecture for which Barcelona is famous? How many sites do you want to go inside, vs. just walk by? That architecture especially appeals to me, so I zigzagged around the city, tracking down a lot of the key sites. I spent 10 days in Barcelona and it wasn't enough. I didn't get to Montserrat, and I missed at least two museums I would have liked to see. Barcelona is a good city for combining half-days in museums with just walking around to see the Barri Gòtic, another historic neighborhood, or the modernist architecture.
In addition to Montserrat, Sitges makes an interesting day-trip, and I thought Girona was worth a couple of days, even without branching out to Cadaques and the nearby Dalí sites. I believe others are happy to spend just one day in Girona.
I think you could spend a great deal of time in Barcelona without being bored, but no doubt you have other places you also want to go, and you likely have limited time available to see them all.
Barcelona is one of those cities where you can't really have too much time (within reason). In 5 days (6 nights) with kids I felt we covered the city fairly well, but we didn't do any day trips.
My husband and I, along with my parents, just wrapped up a two week trip in Spain. We were in Barcelona for four nights and 3 full days. I felt that that was plenty of time to get an overview of the city, including a day trip to Montserrat (left Barca at noon and were back at 19:00).
We were able to see the following, without feeling rushed or overwhelmed:
Sagrada Familia, including tower ascent (advance tickets a must)
Church of Santa Maria del Mar
Santa Caterina market
Picasso museum (audio guide incredibly helpful)
Park Güell (in hindsight I would probably have skipped this in favor of Montjüic)
Ramblas ramble (guided walk from Rick's book)
Barcelonetta beach
Barri Gotic walk
Day trip to Montserrat
We were planning to go up to Montjüic one night but I'm 4 months pregnant and needed a night off :)
There was also a huge festival one day we were there, so we spent some time sitting in a square and watching the festivities. There were many sights we didn't get to, but I didn't feel like we "missed out" on anything, especially because the Modernisme architecture isn't a great passion of mine.
One thing I wasn't prepared for was the heat - even in late September it was quite warm, even at night. I think your plan to take the middle of the day off is very, very smart!
I'll list what we did in 5 days (6 nights). I travel with kids which means we go slower but also spend less time lingering in museums.
-Sagrada Famila
-Casa Mila
-Casa Batllo
-barri Gotic walk - incl Cathedral
-Ramblas walk, with the food market. The famous one. The name escapes me now
-Santa Maria Del Mar (one of my favorite churches in Europe, don't miss it!) and a walk around El Born
-Park Guell
-Montjuic cable car, castle, and magic fountains
-Beach morning
-Gaudi crypt
-one evening food tour
-city history museum
We missed our Picasso museum reservation (long story, kids, our fault). Would have liked to go to the Catalan Art Museum and out to Montserrat.
@Mira, Santa Maria del Mar is also one of my favourite churches. Should you be interested there's a bestseller, the Cathedral of the Sea that portrays a story around the construction of this church in the 14th century.
This year I took the Santa Maria del Mar rooftop tour - recommended. I took day trips to Girona and Figueres (Dali Museums) on separate off-season trips, but in season, you can do both in one day. I still haven't been to Montserrat.
Choose art museums depending on your tastes. I skipped Miro, loved MNAC (and wish I listened to Harold who said to allow plenty of time) and was just lukewarm about Picasso. If you aren't big fans, don't put it on your list (mainly some very early works and lots of cubism). One of the very best things to do is the Palace of Catalan Music tour (palau de la musica catalan).
Walking tours are good. Runnerbean tours were not running when I was there and I've been told they are the best. I was very satisfied with the tours run by the TI.
We spent a month in Barcelona this past August, and was out every day visiting sites, and after a month had just about covered all the "biggies". I love Rick Steves books, but I also enjoy the "Eyewitness Travel" - "TOP 10" books. The one on Barcelona is excellent.plus has a wonderful removable city map inside it.
It will be WARM, especially as you get into July, so try to do most of sight seeing in the morning and take it easy in the mid/late afternoons. Find a nice AC museums for those hours. Montserrat is a full day trip. It is easy to get there, but I suggest getting there early, as the sky-tram line going up there can get pretty long.