That said, if on limited time, definitely see the Sagrada Familia. It was one of my favourite tourist sites in Spain, even beyond just Barcelona.
In the whole of Spain, the south has a significant history with a lot of historical buildings and very old city centers. Sevilla especially, but Granada or Cordoba are gems too - and I'm skipping lots of smaller cities or villages like Ronda, Setenil or Toledo more in the north, each more interesting than Barcelona. Unless of course the goal is to party, then none of the previous villages are very appealing :-)
It's maybe the most heavily planned and designed European capital.
Maybe it's hard to see that coming from the US where all the cities have been planned in the last centuries and you are used to see blocks everywhere, but in Europe it's the exception, and the way it have been done in Barcelona is, I think, unique in the world.
If you don't know the concept of superblocks, there you go : https://www.citiesforum.org/news/superblock-superilla-barcel... but to summarize, Barcelona have been divided in superblocks containing blocks. Inside those superblocks, there are less cars and inside the blocks, there are barely any car at all. What that means is that each superblock is like a little city and each block is like a peaceful village. Hundreds of peaceful places inside of a busy european capital.
It would be fantastic if the whole city was implemented using superblocks, but the reality of it is that the areas where superblocks have been planned go up in price, pushing out low earning locals and bringing in foreigners who can afford it.
This might have been ok for a while in areas like Poblenou which were extremely underdeveloped 20 years ago (mostly industrial buildings) but even the new incarnation of superblocks (green axes) which are mostly about pedestrianization of streets and squares always results in rent increases.
There's no good solution, I would like to see a modern city built with pedestrians in mind from the get-go though.
For example, the Palau de la Música Catalana is amazing, and has lots of the fluid forms and nature iconography you might have assumed was unique to Gaudi, but it's by a different architect (Domènech i Montaner, says wikipedia).
Parc Guell https://parkguell.barcelona/ and La Padera https://www.lapedrera.com/en are must sees for Gaudi
Battló is the best one for me by far. I love the organic shapes and the light well and the soft wood etc. Wow
Today you really have to reserve, sometimes months in advance if it’s during the high season.
Today I wouldn't even dream of that. You really have to plan ahead for all the major sights that include an entrance.
All that said, if they still have the LED-installation at the exit - and if you're like me, and a little sensitive to visual stimuli - avoid that at all costs. It is 360° (or more? I think it's the floor and ceiling, too) of flashing lights and sound, which reduced me to a catatonic state, squatting in the corner with my eyes tight shut and my hands pressed over my ears. It was almost, but not quite (which says something for how good the house itself is), enough to ruin the experience.
I'm biased, but for me it's one of the most beautiful gothic cathedrals in the world, the lights inside are spectacular.