I arrive in Madrid from the U.S. on the morning of April 25. I have this day to do some light sightseeing since I'll probably have jet lag. I have all day on April 26. I've scheduled day trips on April 27 & 28 out of Madrid. I have a few hours in Madrid on April 29 before I leave for Cordoba around 1:00 in the afternoon. I'd like to see the Prado, Thyssen-Bornemisza Art Museum, the Royal Palace, the Sabatini Gardens, Retiro Park, Glass Palace. Do I have enough time for these and are there other sites more worthwhile or that I can add to my limited amount of time?
Also, I haven't purchased a train ticket to Cordoba yet and I just looked at the Renfe site and several trains are already full for Sunday, April 29. I was going to wait until I arrived on April 25 to buy the ticket after I purchased the Tajeta Dorado card. Should I forgo the discount card and buy the ticket now before I get to Spain. Is the Renfe site easy to buy a ticket with a U.S. credit card? I really don't want to use PayPal.