The first choice is either city center (within the old walls) or outside. If you want to be close to everything, you’re going to want to be in the center. As an expat, you want to get the real experience of Sevilla, and for that, you have to be in the center. (Though admittedly the expats with kids all live out in Aljarafe.) The center is safe (and has gotten safer over the years - can’t say how or why since I still never see police anywhere). In our five years, we witnessed two purse snatchings—not bad for a city.
The next question is where within the center. The only shady place (prostitutes, drug use) is a small area right above the Alameda de Hercules. Before I got there, the whole San Luis area was dangerous, so the City Hall just razed it all—the new buildings are almost up.
Anywhere else in the center is fine, and close to everything.
I wouldn’t live right in Santa Cruz—you’ll get tired of the tourists. Right around it, though, is very convenient to everything.
Triana is the real thing, but you might get tired of crossing the bridge every day.
To Camaron!