I've heard of taking the AVE train, but wouldn't I have to somehow get from the MAD airport to the train station?
I am looking for a fast but safe route (I'm not sure how safe the public/city buses are but I am going to have all my travel bags and will look like a huge, foreign target). If possible, I'd like to save money. My flight lands at 1, and I have about 4.5 hours to get from Madrid to Seville, and I have to be in a place called the "Hotel Alcazar" which is about a 10-minute walk from the Seville Cathedral.
Can someone give me the least stressful way to get there? I was thinking maybe just taxi to the AVE, then get off in Sevilla and walk but if there's another great train that's fast that I don't know about please suggest!