Barcelona itineraries fail when they try to do Sagrada, Park Güell, Montjuïc, and a beach day in 24 hours. One timed ticket per morning.
2 nights: the two tickets
Day one: Sagrada Família and Eixample walk. Day two: Park Güell, then Gothic Quarter late. Evening in Gràcia or El Born. This is the add-on after Madrid on a 7-day Spain trip.
3 nights: add a neighbourhood day
Keep the two-ticket core, then a slower morning in Gràcia or Montjuïc, and Barceloneta if the weather is kind. This is the comfortable city break.
With Madrid
AVE 2.5 hours. Do not fly between the two on a first trip unless the train is sold out. See the national itineraries for 7- and 14-day versions.
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