Trip from the airport to the centre of Lijiang:
Take the shuttle bus (CAAC) just outside the airport. It will take you to the centre of Lijiang (30-45 min, 15CNY). From there take a taxi to the Old Town (10 min, 10CNY).
If you're tired, you can take a taxi directly from the airport to the Old Town (30 min, 80CNY).
