Luckily, a lot of the key sites in Madrid are very centralized and since you have a limited time and it's your first time in Spain, you probably just want to concentrate on a few highlights.
I see you're Marriott Gold. There are 2 AC hotels within several blocks of Atocha. It's not a particularly exciting neighborhood, but it's close to Atocha (though that matters more if you're taking the train). Super nice is the Palacio del Retiro, also by Marriott, which is right on the Parque del Retiro and in the same vicinity but much nicer area. The ME by Melia on the Plaza de Santa Ana is a personal favorite.

On Saturday night, I'd get a nice dinner - either at a good sit-down restaurant followed by drinks (you can stay out as late as you want in Madrid!) or do a traditional bocadillo de calamares near the Plaza Mayor or at El Brillante across from Atocha/next to Reina Sofia, and some tapas at a couple different spots. Either late night or early Sunday morning, get some churros con chocolate.

For Sunday, a few things - I suggest checking out the Prado Museum as it's one of the great museums. You could also do the Reina Sofia, particularly if you're more into modern art (Picasso's Guernica, Dali). Leave some time for a walk through the Parque del Retiro (Madrid's Central Park), which is particularly lovely on Sundays. It's also just behind the Prado. The Prado, Reina Sofia and Thiessen museums are all within a few minutes walk from one another. Also nearby but slightly further west are the Puerta del Sol, Plaza de Santa Ana and the Plaza Mayor, worth a walk-through for a first time visitor.

There's much more to see in Madrid, but for just over one day, that's a pretty good start.