Avenue of Stars is about 500 meters to your hotel, you can walk there. When getting to the Peak, you can take Subway Line Tswen Wan and alight at Central Station, after that take bus 1 to the Peak, this will cost HKD16.3, the cheapest way.
To Disneyland, walk to Tsim Sha Tsui Station and take Subway Line Tswen Wan, change to Tung Chung Line at Lai King and alight at Sunny Bay, and then change to Disney Resort Line, costs HKD18.5.
To Central, take Subway Line Tswen Wan to Central Station, it costs HKD8.5.