khars:

I have enjoyed the Hotel Becquer downtown.

Seville old part known as "Casco antiguo" is walkable and buses scarce. Have you yet looked at the map tool on Trip Advisor ? Along with the budget etc tools they are very useful. Zoom into the area surrounding the cathedral. Many hotels and many reviews. I have stayed in several hotels each with own ambience and cost. Last but one in the Adriano which I liked especially as the cost was reasonable when I booked. That is behind the bullring and in quite a nice part of the old town called Barrio Arenal. Another time in the Altimar which is great for its very central location just within a few paces of the cathedral square and although rooms small I found it neat. Another time in the hotel Alcantara which again is near the cathedral on a traffic free street and whilst rooms are small I found it perfect for that stay. I could go on but there are many places to sleep in the old quarter !

Three years ago we stayed at the hotel Amadeus and really enjoyed it. It is a charming small, family-run hotel which is within easy walking distance to the Cathedral and the Alcazar, for example. The manager speaks English and gave us several good recommendations on tapas bars and flamenco. We are going back later this month and will stay there again. Hope this is helpful and that the hotel is as good as we remember!

http://www.hotelamadeussevilla.com/tarifas/

even if you are not going to hotel amadeus, it's always nice to check out the rooftop bar for the views of the Cathedral

My favorite hotel in Sevilla, for both the location and the incredible staff, is the Hotel Alminar. It's small so you don't have the sterile business hotel feel and the staff will go out of their way to help you and make you feel at home.