Madrid has a great public transportation system consisting of buses, metro, and light rail. The easiest way to navigate the city is to buy a Turistico pass, which can be used on all modes of transportation for a certain number of days. It costs €8.40 for one day or €35.40 for five days. Taxis and ride-sharing services are also available at varying costs.
If you have more time, consider a day trip to Segovia, a city with a well-preserved Roman aqueduct and a fairy-tale-like castle. For those with less time, consider skipping the Palacio Real or Malasaña neighborhood. Don't forget to try Madrid's famous Churros con Chocolates, which are best served in the early morning at Chocolateria San Gines.