If you are flying into Madrid, I'd just stay there for the 2 days! You are going to be pretty tired after the flight and I don't know if you will want to just hop on a train and go right to Sevilla! There's a lot to do in Madrid, and it is certainly as safe as anywhere you'd go in the U.S. I haven't stayed alone in Madrid in quite some time, but I have gone there with only my (then) 12 year old as a "body guard!" There are a lot of suggested hostals and hotels on this board that are "safe" ( I stayed at a hotel in Naples once and woke in the middle of the night to find the son of the manager standing at the foot of my bed watching me!
That would qualify as an example of NOT SAFE!)
Have a great time!!!