For me Seville is a more interesting place than can be realised from the top of the Giralda. Locals who are most likely to talk about this are the 'Camareros' (staff) in the local bars. I found out from one of them that many younger people congregate in a neighbourhood called La Alameda de Hercules. There are numerous eateries and bars there, but leave your valuables behind.
Updates
I was in Seville about three weeks ago and the La Alameda de Hercules is currently a huge building site. Looks like a new road is going straight through it. This area is currently a major building site as a new road is being constructed. The bars are therefore less appealing than in previous times. Perhaps by summer 2007 things will be back to normal. The news about the building site is a little out of date. It's now a big plaza, with plenty of bars and restaurants, and even a slide and climbing frame kind of thing for little kids to play on. People hang out here every weekend enjoying a leisurely lunch.
There is a road which goes up the side of it, but it's mostly pedestrianised.
Is this your business?