Every time I have been to Barcelona I visited Park Güell. It is one of those places you cannot really get sick of - situated on the Carmelo hill overlooking the city, this green oasis is an environmental, cultural and architectural refuge.
The park was built between 1900 and 1914, commissioned by Eusebi Guell and designed by Antoni Gaudi, the renowned face of Catalonian modernism. In 1984 it was declared an UNESCO World Heritage Site.
Initially the park was conceived as a high-quality housing project, which however was financially unsuccessful. It was later converted into a municipal garden featuring great examples of Gaudi's architectonic genius; structural solutions deeply rooted in the analysis of geometry and organic shapes, the foundations of what would later become his organic style.
Today the park is mainly a tourist and cultural hub. It's a great place to spend a sunny day while walking through the greenery, enjoying the views and listening to the vast range of street musicians.
For me this was the first time visiting the park during the main tourist season and my advice is to avoid those busy times. Like most of Barcelona, the park is pretty much overran during the months of July and August. Also, it can get quite hot here in peak summer, so make sure you have food and water with you.
There is a cafe in the park, but it doesn't offer much and is horrendously expensive. You will have to buy tickets in order to visit the inner sanctum of the park, which of course is the most impressive part in terms of architecture. Here again make sure to book your tickets in advance as waiting times can be 5 hours and longer.