If you have about a week I would suggest you go to some different countries instead of staying in Spain. In this case the obvious thing to do would be Barcelona - Paris - Londen. You can take overnight trains from city to city to save on accommodation and time.
I do agree that Barcelona is worth a day or four (have been here myself for over 2 months now and still not bored) but if you would take 2 days you can already get some nice impressions. I reccommend the beautiful roof of Casa Mila (La Pedrera), Park Guell (buy a drink in the supermarket in front and not in the park, saves money), Hospital Sant Pau (very close to Sagrada Familia), and sitting down on a terrace next to the harbor on your way to Barceloneta.
In Paris of course you have to see the Eiffeltower, if you want to enjoy the view over the city but not wait in line to long you can climb on to arc de triomph instead, not as high but just as beautifull. Buy some drinks and go up to Montmartre at in the afternoon to watch the sunset from the stairs of the Sacre Coeur and if you have some time left don´t forget to visit the cemetary Pere-Lachaise, very impressive!
Finally in London, if you like markets make sure to go up to Camden lock where there is market all day. You can also walk down in the direction of the center via other markets. If you want to relax for a bit you can take a walk from hyde park into St James park to finally end up at Buckingham palaca where you can have some laughs with trying to get the guards to laugh (never worked for me yet though).
Of course you can also choose to do just two of those cities if you would like some more time to spend in each.
Let me know if you want some more information
OHannemarie
(Oh-Holidays)