I spent some time working Seville, and I absolutely recommend spending a day or two there at least. You can visit the largest gothic cathedral in the world and see Christopher Columbus' tomb. It's pretty cool, and you can go up into the tower and get an amazing view of the city.
Seville is also one of the few places where they still do bull fights, I believe. I caught one while I was there and while it was certainly somewhat disturbing, it was a really cool cultural spectacle that I'd recommend you see if possible.
Speaking of Game of Thrones, they're using some location in/around Seville for filming, so you could check out Dorne. I can't remember offhand the exact location, though.