In the morning, we went to the Picasso Museum and bought tickets for entry in the afternoon. The number of people that can enter at the same time is controlled due to the popularity of the museum. We spent about an hour and a half in the museum.
In the afternoon, we walked from the Picasso Museum to La Sagrada Familia which is about 10 blocks away but an easy walk through El Eixample which is the modern part of Barcelona.
Later we also went by the Arco de Triunfo near the Parque Ciutadella.
Even in May Barcelona is packed with tourists and all of the attractions are usually full of people.