Flights: ČSA offers direct flights to Madrid. A flight for two in November was a little over 10,000 CZK. A search on Studentagency.cz led to flights from Lufthansa, Swiss air, and Brussels Airlines for around 11,000 CZK. (Wizz air offers flights to Madrid, but unfortunately it seems like there has been an interruption to their flight schedule in October and November.)
Once arriving at Madrid Barajas airport there are several options for getting into the city center. Take the underground (line 8) for 4.50 EUR. Take one of several bus options, including the Airport Express bus for 5 EUR or a city bus for 1.50 EUR.
Where to stay: The Chueca district, just north of Gran Via (Madrid’s main boulevard), offers some budget and mid-range accommodation and is close to some of the city’s best parks: Casa De Campo and Parque del Retiro. The Huertas district, just south of Chueca, offers some budget-friendly boutique hotels including Hostal Adria Santa Ana (hostals aren’t hostels, but rather pensions), which I can personally recommend.
Autumn Events: Estampa (October 25-28), Madrid Jazz Festival (Nov)