We just stayed there for 3 nights post-transatlantic. We chose an AirBnb in the Gracia neighborhood and it was amazing. Somewhat removed from the tourist crush but vibrant and so many things were an easy walk, plus the metro is easy to use to get around if needed. We saw only a taste of what was there but had a very enjoyable time. Leave yourself some time to grab a bite or coffee in a nearby plaça and enjoy life like a local. Another tip: several tourist attractions sell tickets online in advance and do sell out, so do some planning ahead for those. We were unable to see inside La Sagrada Familia because the tickets were gone for that day. (Good reason to go back, though, right?)
Something I did not know: Barcelona is located in Catalonia, which is kind of its own part of Spain. A decent percentage are pushing for independence. Their first language is not Spanish but Catalan, which is not a Spanish derivative. Most do speak Spanish, but learning a few survival words/phrases in Catalan is quite helpful.