Great place to be stuck if you happen to have somet time to wait, my favourite coffee shop is Joe and the Juice but there also many great shops from Danish designers!
Wifi costs 80 ddk (~11 euro) for 4 hours. Works fine in most cafes and lounges while you wait for your connection. There are 30 minutes and 1 hour tarifs too.
Great airport, navigation is simple, reaching downtown is fast. The check-in lane is extremely long and slow. It is not the best airport among nordic states.