Barcelona in two days
The second day unlocks what the first doesn't touch: Park Güell and the Carmel viewpoints in the morning, Montjuïc and its museums in the afternoon, and the night among El Born's terraces or a rooftop.
Day 2, morning: Park Güell and Carmel
First slot at Park Güell before the crowds, walking down through the free paths to Gràcia, where vermouth and squares are the reward. The Bunkers del Carmel as the viewpoint finale.
Day 2, afternoon: Montjuïc
Funicular from Paral·lel, the MNAC or the Miró Foundation by appetite, and the palace staircase at sunset with the whole avenue at your feet. Castle and garden cemetery if there's fuel left.
The crowning dinner
Second night, better neighborhood than center: tapas on Carrer de Blai in Poble-sec or a long dinner in Gràcia. Both sit on the way back from Montjuïc and the Carmel respectively.