While visiting Seville in October 2005, we stayed in the Barrio de Santa Cruz, which is a beautiful neighborhood of shops, hotels, cafes, bars, and restaurants in the heart of the city and very close to the Cathedral and the Alcazar. Never once did we feel unsafe. From what I've seen and heard, I think Seville is as safe as any other European city. I would highly recommend staying in the Barrio de Santa Cruz.

As for hotels, we had a wonderful room at Hotel Amadeus (highly recommended) for 90 Euros, but there are many other hotels in the neighborhood that our travel books (Rick Steves' and Lonely Planet) identified that have rooms in your price range.

Enjoy your trip, Mark in Philadelphia