Montjuic - relaxed and scenic
To enjoy a more relaxed night, without discos or people, I recommend Montjüic which has the best viewpoints of Barcelona. Go in the late afternoon and see the city lights below at night. It is really spectacular and very romantic. In Montjuic you will find the famous "Fuente Magica” or magic fountain, which at night has a beautiful illumination show.
There are numerous attractions to visit, such as "El pueblo español", or also a cable car that goes up to the famous castle of Montjüic.
Central yet hidden
There is a charming place that few tourists know, as it is somewhat hidden. It is a bar called El Bosque de las Hadas (Forest of the Fairies) near Ramblas. It is next to the Museo de Cera (Wax Museum). This bar has a decoration and spectacular atmosphere, as if you are in a magic forest. The lighting is very dim, so it is a spectacular experience.
Barceloneta - expensive but worth it
There is a lot of variety of pubs, bars, etc. I recommend Opium, which has areas to be more relaxed having a cocktail, and the "Shoko" lounge with Asian influences, where you can also taste Japanese food. They are not cheap though!
Marina - alternative and affordable
In Marina are the most economically priced places to spend the evening. L'Ovella Negra or Razzmatazz are very alternative places where all kinds of people meet. In Razzmatazz there are often many concerts by very famous rock or indie groups (for example Coldplay).
If you want something more original, there is the Yoga Weeks Barcelona center that is located behind La Boqueria market, in a nice modernist building (very typical of Barcelona) that offers a real urban retreat. You will practice yoga on a beautiful roof, and even taste genuine Bruch. It has highly qualified teachers.
If you're a fan of gin-tonics, this is your place. It has a menu with about 40 brands of gin (Premium).
It is located in Gràcia.
It is considered one of the best bars in Europe! It is a private cocktail bar that needs a reservation by phone. There is live music every night (especially Soul or Funk). I recommend one of their best cocktails, with white chocolate, champagne and bourbon.
If you are in Barcelona on a Wednesday, do not forget to visit the "event room" of this restaurant. In the back of the house there are beautiful recitals of poetry, music, literary gatherings ... it's free and you can enjoy a beer or a typical tapa while you enjoy the event.
It is located in El Raval, near the Museum of Contemporary Art of Barcelona.