I just returned from a month in Spain... Madrid is a lot of fun, you will enjoy it!
There is a new bus service from the airport that makes a few stops in the city center, definitely take that vs. the new subway because its more direct. Its a yellow bus that picks up from both T4 and outside T2.
As far as tapas go, I love the calamari... jamon is fantastic, and definitely try the octopus... with local beer. (Mahou)
Wish I could join you guys but I'll be doing dim sum in Singapore finally