I'd recommend adding these very important places:
- Hospital Sant Pau
- Museu Nacional d'Art de Catalunya
- Palau de la Música Catalana
- MUHBA Plaça del Rei (underground Roman Ruins and medieval Royal Palace)
- Explore Gracia neighborhood (Casa Vicens de Gaudí)
These places you already list I feel are a bit overrated:
- Cable Car Ride
- Las Ramblas
- Parc Guell
Take a look how Rick Steves has his 4 days in Barcelona organised, I think it will give you some good ideas (I flipped day 3 and 4, felt it was better to do the day trip on 3rd day):
Barcelona in Four Days
Day 1 — Old City
9:00 Follow my "Barri Gòtic Walk" (a self-guided walk you can find in my guidebooks) and tour the cathedral.
13:00 Grab lunch in El Born or the Barri Gòtic.
14:00 Tour the Palace of Catalan Music in El Born (advance reservation required).
15:00 Explore El Born, and visit the Picasso Museum.
Evening For an early dinner, sample tapas at several bars in El Born (or the Eixample or Barri Gòtic); to dine at a restaurant, go when locals do, around 21:00. Evening activities include sightseeing (some sights have late hours on certain nights of the week), concerts, or hanging out at a chiringuito beach bar in Barceloneta. Another fun evening activity is to zip up to Montjuïc for the sunset and a drink on the Catalan Art Museum's terrace, then head down to the Magic Fountains.
Day 2 — Modernisme
9:00 Check out the Eixample (you can take the self-guided walk in my Barcelona guidebook — or in my Pocket Barcelona guide), touring La Pedrera and/or one of the Block of Discord houses — Casa Batlló or Casa Amatller (by guided tour only).
12:00 Eat an early lunch in the Eixample, then tour the Sagrada Família - add Hospital de Sant Pau.
14:00 Choose among these options: Taxi or bus to Park Güell for more Gaudí. Or take the bus to Montjuïc (if you're not going to Montjuïc on Day 3) to enjoy the city view and your pick of sights. Or explore the harborfront La Rambla de Mar and Old Port (unless you already did this on Day 1, at the end of the "Ramblas Ramble").
Day 3 — Day Trip
Consider a day trip to the mountaintop monastery of Montserrat, the beach resort town of Sitges, the Salvador Dalí sights at Figueres and Cadaqués (reserve both in advance) or the seaside Roman Ruins of Tarragona
Day 4 — Montjuïc and Barceloneta
Morning Tour Montjuïc from top to bottom (both physically and in order of importance), stopping at these sights: Fundació Joan Miró, Catalan Art Museum, and CaixaForum. If the weather is good, take the scenic cable-car ride down from Montjuïc to the port, and spend the rest of the day at Barceloneta — stroll the promenade, hit the beach, and find your favorite chiringuito (beach bar) for dinner.