By the time you arrive in Madrid you may indeed find yourselves exhausted and need some downtime! Once again, end of August in Madrid will be super hot! I suggest you get an early start if you want to visit places outside of Madrid and be back in the early afternoon to relax/recover.
Drink loads of water and be happy with one trip outside of Madrid-Segovia and La Granja would be my suggestions!

Toledo, without a doubt from my perspective. But, consider doing it as an overnight. It is really quite charming after the daytrippers leave. I spent 3 or 4 nights there.

I did Cuenca as a day trip from Madrid. Enjoyed it but loved Toledo.

Another vote for Toledo.

Tons more to see in Toledo.. no comparison. It used to be the capital of Spain.. so it is laden with wonderful buildings and the cathedral and churches and once-convents.

OK, so if we must choose ONE day trip from Madrid -- Toledo. If we have the time and desire to take 2 trips -- Cuenca.

I loved Toledo, but thought it deserved 2 full days. Many people go for just a day trip.

I home exchanged in Salamanca last year. I would not do Salamanca as a day trip from Madrid. The problem with rail passes is that you always try to "max" them out and you end up spending too much time on the train. Madrid is an interesting city by itself and, at the end of the trip, I spent 4 days there. If you like art galleries, it's a paradise.

Here are links to my blogs on my website from last year from my trip to Salamanca and Madrid:

http://altecockertravels.weebly.com/...ghtseeing.html

http://altecockertravels.weebly.com/...es-madrid.html

http://altecockertravels.weebly.com/...nd-madrid.html

http://altecockertravels.weebly.com/...ht-ventas.html

http://altecockertravels.weebly.com/...ht-ventas.html

http://altecockertravels.weebly.com/segovia.html

http://altecockertravels.weebly.com/...-aranjuez.html

The one place I did not see that is on everyone's list was Toledo, so I can't offer an opinion on that. I also did not get to the walled city of Avila, but just saw it from the road. As with everyone else, I had to make choices and ran out of time. The thing I loved most in Spain was the food. Oh boy!