Sure is Quiet!
Hey, I'm busy WORKING to pay for this vacation! ...and making my must-see list for Barcelona. It's too long
In geographic order

lmao: ):
Barri Gotic/La Ribera/El Raval:
Catedral (8-1:15 & 5-7:30 free, 1:30-5 4 Eu)
Museu d'Historia de la ciutat (10-8 Tu-Sa 10-3 Su, 4/2.5 Eu)
Las Ramblas from Columbus statue to Placa Catalunya
Palau Guell (10-6:16 M-Sa 3/1.5 Eu)
Eglesia de Santa Maria del Mar (9-1:30 & 4:30-8 daily, free)
Eglesia de Santa Maria de Pi
Parc de la Ciutadella/Arc de Triomf
Museu de la Xocolata (10-7 M-Sa 10-3 Su, 3.8 Eu chocoloate workshop tour ?)
Museu de la Geologia
Eixample:
Sagrada Familia (9a-8p 8/5 Eu lift 2 Eu 3 Eu guided tour)
Manzana de la Discordia
La Pedrera - roof (10a-8p, 7/3.5 Eu)
Casa Battlo (9a-2p M-Sa, 9S-8p Su 10 Eu, 16 Eu incl roof) the dragon
Casa de les Punxes
Palau de la Musica Catalana
Port Vell:
Montjuic, Castle, Village & Teleferic
L'Aquarium
Parc Guell
Montserrat