Had a fantastic week in Barcelona – no problems at all – the only precaution you should take as with most tourist traps is not to take expensive jewellery/watches. Just enjoy – in no particular order
Sagrada Familia,
Camp Nou
Olympic Park
Tibidado
The Beach
Fruit and Veg Market just off Las Ramblas
If you have more time
Science Museum (on the way to tibidado)
Picasso Museum
Parc Guell