I will have about a 22 hour layover in Madrid. I arrive at 7:30PM on a Saturday and leave the next evening (Sunday) at 5:00PM.

My hotel is in Puerta del Sol. I'm thinking that I should just stay around that area for the night and then visit the Prado museum in the morning.

After the Prado, will I have time to visit the Royal Palace as well, or will my time be severely limited?

Thanks.

Obviously it depends on how long you stay at the Prado. the two sites are not a great distance apart. It would also depend on if you carry your bag with you or need to return to your hotel.

I would suggest buying a ticket on the hop-on-hop-off tour bus (Madrid Vision)
http://www.madridvision.es/en/index.php

Thanks for the bus link, jeff001.

weber6560, I really don't know how long I will stay at the Prado. Probably not too long. I do have a major interest in pre-20th century European royalty, which is why the Royal Palace appeals to me, but if I missed out on the Prado, I think I'd regret it.

I do not what the experts will tell you, but the Prado for me is beautiful, nearby is the Jeronimos church, a royal church where I believe Alfonso XIII was married with Victoria Eugenia. The Palacio Real years ago had opened to the public the very interesting private apartments of this Spanish King. Unfortunatelly I do not know if they are open to-day. IF your hotel is in Puerta del Sol vecinity, you will be fairly close to the Palacio Real and also to el Prado, but take a taxi to save time. At least I would.
The Prado is free on Sundays.