What is the best route if via MRT or bus from Tsim Sha Tsui to Lantau Island?

Hey, MTR is recommended. You may walk from Tsim Sha Tsui to East Tsim Sha Tsui Station and take West Rail Line. Get off at Nam Cheong and transfer to Tung Chung Line. You should get off at Tung Chung Station. Then leave from exit B and catch the cable car up to the mountain.

You are suggested to visit in the morning to breathe the fresh air there. If you wanna see more, head for the Disnyland and stay there till night after the Lantau Island.