If you're flying into Madrid, then you'll probably be arriving at Madrid-Barajas Airport, Torrejon. There are usually buses or trains at the airport that can take you into the city centre. Check out how to get to your accommodation from whichever airport you will be landing in to ensure that you settle in smoothly.
There are plenty of great museums to visit around Madrid, such as Thyssen-Bornemisza Museum, Museo Nacional Centro de Arte Reina Sofía, Museo Nacional del Prado. Make the most of your time by having a look at what interests you beforehand. Why not bring the whole group along with you?
Madrid has already hosted some of the most memorable nights in sporting history. You may have heard of stadiums such as Santiago Bernabéu Stadium, Vicente Calderón Stadium. Many of them offer tours too!