Barcelona is an amazing city. So much to do and to see, with beautiful architecture. Three of us spent 6 days in May a few years ago. They say May-June is a good time to visit, as it is not too hot, and not too crowded. We rented an apartment that was pretty close to Sagrada Familia, a good neighborhood, and not so touristy location.
We walked a lot and used a cab when too tired to walk back. Cabs are pretty affordable, and for 3 of us, it was comparable to using public transport. We also used the Hop on Hop off bus for a couple of days, which gave us a perfect opportunity to see the whole city and decide all the places we wanted to spend more time in. I highly recommend it. Here are some highlights and must-see while in Barcelona.
Sagrada Familia - basilica designed by famous Antoni Gaudi. It is still under construction, and it has been for over 100 years. It is the most beautiful architecture I have ever seen. Absolutely it makes you breathless. The beauty with all details is just difficult to put in words. The tickets were about 20 euros. We bought our tickets online and did not have to wait in line to enter. Highly recommended, if it is still an option.
Park Güell is another must-see when in Barcelona. It is a very unusual, colorful, and fun place to visit. Pay attention to the longest bench and visit Gaudi's house. I believe there is an entrance fee of 10 euros.
La Rambla street - is a famous pedestrian street in Barcelona. It starts at Plaça de Catalunya and goes to the seafront. It is very touristy, and not my cup of tea. All the reviews indicate pocket-picking, and definitely something to be aware of. I would not recommend eating in the restaurants in that area either. One of the side streets will take you to the famous food market La Boqueria, which is another have-to visit spot.
A Gothic quarter (Barri Gotic) - probably my favourite spot in Barcelona. It is a quarter with narrow streets, lots of squares, restaurants, cafes. There is a beautiful cathedral and the Picasso Museum. You will also find many unique local boutiques and shops.
Magic Fountain of Barcelona - spend some time enjoying those beautiful fountains. It is a magic of colors, music, light.
Montjuïc - you can use The Port Vell Aerial Tramway to reach to Montjuïc. You will find here lot of great artwork, but the view of Barcelona is simply spectacular.
Beach Barceloneta - you will find this beach at the end of the La Rambla. Very nice area to walk and to enjoy. There are lots of good restaurants in this area as well
Salvador Dali Museum is a couple of hours drive from Barcelona, and is located in Dali's hometown Figueres. On a rainy day, we decided to take a day trip and visit the museum. It was a very good decision with very unique experience. It is definitely worth visiting.
Shopping - there are few good places to shop in Barcelona. I personally like local boutiques in the small streets. The best were El Born, Portal de l'Angel, Carrer d'Avinyo. You can also visit Maremagnum located in Port Vell with some typical brands, and a few nice restaurants with a great view of the sea.
Restaurants - in general food and wine are great and pretty affordable. We stayed away from touristy places and restaurants and picked local places. You can't go wrong with tapas in those places. Few great restaurants were in the area close to the beach with lots of seafood.
There are many other places and buildings to see if you can spend few more days.