11 Days in Barcelona mid March with my 21 year old daughter. Advice please.

Besides the Sagrada Familia, we enjoyed the tour of the Palau de la Musica Catalana

In which neighborhood would you recommend I rent a two bedroom apartment?

The Barri Gotic!

intersted in history, art, architecture

Take Rick Steves self-guided walking tours and visit the Picasso Museum and the Sagrada Familia (buy tickets in advance for the latter). I would also purchase tickets ahead of time for the Dali Theatre-Museum in Figueres which you can take a direct train to departing from the Barcelona Sants station to the Figueres Vilafant station (1h) and then hop into a taxi to get to the theater. I would also take a day trip to Montserrat.
Rick Steves guidebook on Barcelona (fifth edition) will give you much more information on how to stay occupied for eleven days than this forum will.

I have been to Barcelona several times and truly enjoyed two specific Gaudi sites: La Sagrada Familia and Park Güell. I am a huge Picasso fan and enjoyed the Picasso Museum. My husband who is not a fan and really didn’t like the fact we went on a free day liked the museum. It is small and shows the evolution of Picasso’s art from his youth to older years. My husband really liked the ceramics.

For something a bit different, you may want to take a food tour or cooking class. I would highly recommend Cook & Taste cooking school. You will first go to the Boqueria Market to shop for ingredients than make a few tapas, Paella, and dessert. It is a half day, but definitely a memorable experience. For a cooking tour, I would recommend Devour. They have evening food and wine tasting tours.

Have a great time.
Sandy

In addition to the other comments here, my husband and I greatly enjoyed a walking tour of Barcelona. I cannot recall the name of the company, but we paid at the end what we determined to be a fair price.
We stayed just one street away from La Rambla but it was a very quiet two-bedroom, one-bath flat. It also had a washing machine on the roof of the building (!) which we used.
Spanish food was quite good. I especially liked the bread which was toasted and rubbed with raw tomato and garlic which was served in most restaurants and massive amounts of beef (I usually don't like meat). I am very particular about my coffee and Spain did not disappoint--second only to Italy, in my opinion. Spain also does chocolate very well (churros are a must at least once). Perhaps my fave was patatas bravas with its spicy kick. Don't forget to order Tortilla de Patatas for breakfast or anytime.

I did not experience great wine in Spain but, perhaps, that was just my lack of knowledge of good wine there. I did drink my fair share of cava which was nice and quite reasonably priced. As a matter of fact, Spain was quite cheap compared to England, France and the rest of western Europe.

We stayed in the Gracia neighborhood. We walked everywhere from there and it is far less touristed and more neighborhoody than some others

There are countless awesome things to do near there. I can tell you the things we did that we loved doing and that was an overnight at Montserrat (staying one night was really key; opened up many opportunities that the day-trippers missed), a few nights (though it's only an hour by train from Barcelona) in Girona (much smaller, more easily-digestible medieval city with amazing history), and a fun day-trip from Girona that could also be done from BAR is to Figueres for the Dali Museum.

Those are the things around BAR we did that were all terrific. All the other suggestions are terrific, too.

Again, great suggestions for day trips as well as things to see and do in Barcelona. Just to add… we took a great bike tour of the city with Fat Tire Bikes. Lots of fun!

Go up on Montjuïc for beautiful views of city and sea and visit the Musee Miró . Don’t miss the section with his whimsical art up on the roof.
Day trip to Musee Dalí in Figueres.
We liked staying in the Eixample district.

I would second the suggestion to spend some time on Montjuic. Great views, great park to stroll, good museums. Could spend a full afternoon there.

My wife and I also did a day trip to Tarragona--we enjoyed it and would recommend. It's close by, so not too much travel time, and the Roman ruins (aqueduct and ampitheater) were a welcome change of pace to a Barcelona visit (although there are a few Roman-era sites in Barcelona).

Definitely do Montserrat. It was nice to get up into the mountains, and the monastery is memorable. We rented a car, and wandered some of the mountain villages for a few hours--nothing listed in any guidebook. Loved it.

We spent about 2 days just visiting the Gaudi sites--and there were more that I wished we had seen.

We found a local bakery near our hotel that we liked and visited every morning for breakfast. Started to recognize a few of the regulars--made us feel like Barceloners.

Rick's guidebook should do you well.

Enjoy your stay and time with your daughter!

You will love Barcelona! It's a wonderful city with so many interesting sites.

I agree with the poster who suggests staying in Gracia. It is a "real" neighborhood where people live and children go to school. We spent some time there wandering around and had lunch. Not touristy at all. I also recommend staying in Eixample. It's a lovely area with beautiful architecture and close to many sites. Within walking distance of Casa Battlo and Casa Mila (La Pedrera), two important Gaudi sites. We stayed in Eixample in 2010, and I remember it as being quiet at night.

Since you do have 11 days in Barcelona, another suggestion would be to take the train to Girona, either for the day or an overnight. It's a medieval walled city on a river, with narrow winding lanes, so interesting to visit.
https://www.earthtrekkers.com/best-things-to-do-girona-spain/

The official TI website is the best way to look for what to see and do and eat and drink in and around Barcelona.

Day trips I did - Tarragona - I went mostly for the Roman ruins which were a huge disappointment but I liked the town. A good part of the train ride was very scenic along the Med coast. Be sure to have a glass of vermut while you're there. Girona is a good day trip, interesting medieval Jewish area and very good Jewish museum (a lot about daily life in medieval Spain), and the cathedral cloisters were beautiful. Figueres, for the Dali House and Jewel Museum is excellent as well. Nice town to wander a bit as well.

I'm not a fan of Gaudi but I love many of the other moderisme sights - Palau de la Musica, Sant Pau (15 minute walk from La Sagrada Familia). You can see bits of moderisme eveywhere if you know to look. Take the TI's walking tour.

Another highlight for me was the rooftop tour of the Santa Maria del Mar church. All the old churches are interesting. MNAC is an excellent art museum - allow at least a half day there.

Since you're staying in an apartment, you'll want to buy some provisions. El Corte Ingles on Plaza Calalonia has a basement full of ready-to-eat choices as well as a huge supermarket. While La Boqueria market is a tourist attraction, the nearby Santa Caterina market is where locals shop. Across the street from the main entrance is one of my favorite bars, Orio, with a great selections of wines and pinxos (the Basque equivalent of tapas). You'll find other Orios in Barcelona and maybe other cities as well.

The 1-euro city map I bought from the Tourist Office in 2016 had a lot of modernista buildings marked. (If you see something on the map that's not identifiable as something like a museum, it may be there because of its modernista facade. I enjoyed just wandering around, finding those cool buildings.

Thanks to all for your thoughtful advice.
Chani, you mentioned that Tarragona was a huge disappointment for you.
Could I ask why please as it was on the short list for a day trip?

In addition to everything already mentioned, there are some very good, inexpensive guitar concerts in the 15th century Basílica Santa Maria del Pi, https://www.maestrosdelaguitarra.com/concerts-en/

@jkin101937, my dear friend Channi (honest, we're good friends!) didn't like Tarragona cause she comes from an area of the world where Romans also "settled" for some centuries and her motherland contains tonnes of great Roman ruins... so, in a manner of speaking, she needs something much more extreme to be impressed, right Channi? LOL!.

But again, (seriously speaking now), Tarragona -known as Tarraco during the Roman Empire- was the capital city of the huge Tarraconensis province, which covered two-thirds of the Spanish peninsula and as such enjoyed many centuries of richness. This turned the city into a fully-fledged major Roman city in the Empire which harboured: a typical city wall, amphitheatre, citadel, Pretorium, necropolis, palaces, an arch, and obviously, a circus. There is a good reason why Tarragona was declared "World Heritage City" by UNESCO in 2000. So, if you come from an area that wasn't touched by the Romans, Tarragona is bound to impress you.

Yet Tarragona is not only worth visiting because of the Roman heritage but also for several other features: its Cathedral, built in the 12th century on the site of a 10th-century Moorish mosque; the heritage festivals, the old fishing village of El Serrallo, etc.

https://patrimoni.gencat.cat/en/collection/tarraco
https://www.tarragonaturisme.cat/en

Also just outside of Tarragona is an Ancient Roman aqueduct called Les Ferreres Aqueduct that one can actually walk on top of like a bridge, that certainly makes for a unique experience not many can boast about!

You can read more about it here: https://www.catalunya.com/les-ferreres-aqueduct---pont-del-diable-17-16003-10?language=en

LOL thanks to my dear friend Enric who has helped me so often to enjoy his beloved city. Everything he says is true about Barcelona.

Yes, my country is littered with Roman ruins, but not nearly as much as Italy (though we have a lot of other interesting ruins worth visiting). I went to Tarragona for the Roman ruins, sigh. Once I got over that disappointment, the town was quite nice, but my memories are a bit blurred, perhaps because I had two glasses of the local vermut (it's a tad strong) and my memories of the sights in Barcelona and Figueres (Dali) are much stronger. There were interesting medieval sights in Tarragona, though.

I haven't been to Zaragoza yet, but it's been at the top of my list for my next visit to Barcelona (no plans but lots of hope).