I don't know what you are looking for but as for me
I like to go rock climbing in Mont Juic.
I like to go to the Tibidabo by foot, you can take the metro and then walk in the forest/mountain. (it's a 30 min walk). There is a great view and you can go down with the funicular
Next to the Museum of contempory art, there is a museum which is way more interesting (according to me) which is called the Centre de Cultura Contemporania de Barcelona. Sometimes in the summer they boradcast movies outside.
I like to do some longboard/roller on the walk in barcelonetta close to the beach
I like to have a beer en la oveja negra with some friends en el raval and eat tapas in the bar in the corner.
I like to go at the Felip Neri place in the Barrio antiguo. In this place republican, anarchist and other undesireable people were executed during the civil war. You can still see the bullet scarce on the wall
The sunday in Gracia there are Lindy Hop/swing dances
Well there are lots of things to do, you can also walk and lose yourself in the city and discover your own part !