Recently I booked a flight for Madrid for 10 days. I was supposed to take a flight to another part of Europe but then prices got really expensive. Now I think I'll be staying in Madrid for those 10 days. Any reccomendations of what to do?
Madrid for two weeks
This may help; https://www.travellerspoint.com/guide/Madrid/
If you really want to explore someplace else, you could consider the train. It's usually cheaper than flying and a lot more comfortable.
Just a thought. Enjoy Madrid.
The train is a good option if you want to get out of Madrid. You could also hire a car and explore around Spain. Car hires aren't that expensive in Spain. If you want to base yourself in Madrid you can add some day trips as there is plenty to see around Madrid. You can visit Toledo, the Royal Monastery of San Lorenzo de El Escorial, Segovia and Avila. It would be even feasible to do Salamanca or Valladolid as a day trip though it would mean an early start. If you like the outdoors you could visit Parque Regional Cuenca Alta Manzanares. They have some nice hiking trails.
It one time, you could take a sleeper from Madrid to Lisbon, Not sure if you can do that anymore, but if you can, two weeks would be a short time. And I've also taken a train to Valencia and to Granada.
Train is a good option as mentioned earlier. There various LCC options out of MAD and I'm sure you can pick up some random destination to explore for few days. 
Toledo, Segovia and Avila are all great options for day trips from Madrid.
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Of course, train is a good option to visit places in Madrid but you can also enjoy car riding because it’s not so expensive in Madrid. Happy travelling!