Hello, what is the best way from Beijing International Airport to Swissotel Hotel?

Yes, there will still have official taxis at the airport that can take you to the destination.
The pick-up stations are Outside Gate 1 on F1 of T1; Outside Gate 5 to 9 on F1 of T2; In T3, Please refer to the signs inside the terminal building. Generally speaking, you don't need to worry about the safety problem. The cab fare would be CNY 90 to 100 at that time.