Not really a 'must see' while in Barcelona - but Placa Reial is a very beautiful square, and if you have time, you should check it out.
I was lucky enough that the hostel I was staying at was situated in one of the buildings around this square. It is filled with cafes and restaurants, and is a great place to grab a meal and relax.
Or an alternative is to just buy a drink, sit against the fountain or on one of the seats around the square and just people watch. It really is like a picture from a postcard :).
Placa Reial is found about a third of the way up Las Ramblas on the right (if coming from the harbour).
Placa Reial in Catalan
Plaza Real in Spanish
Royal Square in English
Whatever language you use to name it, it is a beautiful and elegant square great for just having a rest, getting something to drink or eating in one of the restaurants in the vicinity. This is defiantly one of my favourite Squares in the city.
Fondest memory: I remember my first night in Barcelona we went to a restaurant in the square and that is where I sampled my first Crema Catalana (Catalan Cream) pudding which is one of the most traditional desserts from the region. It also comes in alcoholic drink form mind! It is very sweet but has a nice flavour to it! You must try both the pudding and the drink if you come here! Don't get the pre packaged Crema Catalana pudding though as it is not the same as a home made or at least restaurant chef made one!
Fondest memory: ...strolling streets (and squares) of Barcelona is a pleasure. On the picture - Placa Reial. Laid out in 1850s, the Italianite square is sudded with tall palm trees and decorated iron lamps (by the Gaudi, of course). They say, there is a coin and stamp market on Sanday morning (10 AM - 2PM). The small streets stretching toward the sea from the square are intriguing but dangerous.
Favorite thing: Plaça Reial is the most busy square of Barcelona dating back to 1850. The lanterns were a project of who else, but Gaudì.