What PP said...Sunday , in any city, is a perfect day for museums since most close Mondays

Hmm-Be careful w/Tirso de Molina area it changes very quickly into Lavapies in which I would never stay or walk at night! What street is the apt?
I never take the train to Toledo or Segovia.The cooach bus is easier-it drops you off in the center of town.You will need to take a bus or taxi from the train stations.
My take on Toledo vs. Segoviaegovia is a 'happier' place and easier to find your way up from the aqueduct and walk up to the castle.Toledo is a more serious place.
You could actually do both if you got an early start-about 9.
Madrid is an easy city to walk around but if you want an overview then I suggest the on/off bus.It has 2 routes and fun to do especially when it gets dark and lots of the buildings are lit up.

Agree with PP.
Would not stay near Tirso de Molina
Link to the apt?

Madrid is a beautiful city full of lovely neighborhoods.
Why people choose to stay in in unattractive and , sometimes, not safe part of the city is a puzzle.

I am sorry, did not mean to be harsh, but that part of Madrid, although central, would not be my choice to stay in. Lavapies are is known as an poor immigrant and , sometimes, crime ridden part of town. Why stay next door.

As chpla said, it is an iffy area...you can see the street on google. ( a bit run down, graffiti on the walls..etc)

Take a look at Spain Select - much nicer apt. in better location.

here is the web page. We used them twice.

http://www.spain-select.com/en_US