Just got back from Barcelona today after spending a week there on business. Got out on the evenings and on the weekends and my top 3 places to visit are:
1. Segrada Famillia - absolutely stunning outsie, even more impressive inside, just watch for beggars claiming they need to support their children as they are often accompanied by pick pocketters.
2. This one is an absolute MUST: Tibidabo, to the west of Barca, up on the hill. You will see a large church on top of the hill to the west, which you can go up to via the funicular. The views at the church look out over ALL of Barcelona, which are amazing, but even more amazing from the top of the church tower, which you need to pay 2Euros for, but it is well worth it. Fantastic place.
3. The castle at Montjuic, go, see the castle, have a beer, admire the view and relax, definately take the funicular from Paral-lel and then the cable car from there to get up to the top though, saves a lot of walking effort.
The picture below taken by another user is taken from the top of a shopping mall near Espanya metro station, looking out towards the National Art Gallery and the Magic Fountain (which is stunning on a nighttime by the way, but beware, it only works on Friday and Saturday nights). Wait till its starting to get dark and head up there and just sit on the steps leading up to the gallery and admire, its brilliant. When I went there there was a Harley Davidson convention so there were loads of stalls in the area leading up to the fountain selling bike equipment, beer, BBQ food, everything, not to mention thousands of Harleys! Amazing atmosphere with loads of bearded Spannish bikers wearing leather saying "Valencia West Chapter" on them, confederate flags etc! and made the fountain are even more special (the weekend before, it was a gay pride parade! So its entirely circumstantial!).
Overlooking Plaça Espanya towards the Magic Fountain of Montjuic and MNAC.
Now for the warnings:
1. Barca is pick pocket central so gaurd your posessions at ALL times. Particular areas to watch out for are on La Ramblas and the surrounding Gothic Quarter and Segrada Famillia. The small streets, tourists are a magnet for people selling **** who will be looking where you keep your wallet. Areas which aren't too bad are around Espanya, the art gallery and Olympic stadium and the castle.
2. La Ramblas after dark, its not too bad on the face of it, but it certainly aint that pleasant past 11pm, prostitutes, North Africans selling beer cans and samosas, just stay away.
3. To eat, avoid La Ramblas as a rule, too expensive, as is the bit besides the marina towards Barceloneta metro, towards the beach is a little better priced. We found a great Tapas place near Poble Sec metro called "Lolita" or something like that, full of locals only and great tapas and reasonably priced.
4. I'll say it again because its worth saying, distribute the money evenly between your party and only take out enough to cover your day. Don't put it loosely in pockets, don't take your wallet. I used shorts with many pockets and buttons to close the pockets, so I distributed things evenly over the pockets and buttoned them up. Don't wear your camera round your neck. Be especially careful when getting onto the metro and try to stay in the less crowded bits with your back to the wall. Saying all that, I wasn't bothered by crime and no point did I feel uneasy or threatened apart from one occasion when returning on the last metro to my hotel which was full of a few rough characters. Don't be intimidated and have a great time!