To Ocean Park, you can take bus 171 from NELSON STREET MONG KOK/
Bank Centre, Nathan Road to Aberdeen Tunnel Toll Plaza, then walk to the ocean park.
To the peak, you can take MTR from Mong Kok Station - D3 to Central Station - J3, then take bus 1 to the peak. Get down the peak road, you will come to the victoria harbour, there you can see the symphony of lights.
To Wong Tai Sin, You can take MTR from Mong Kok East Station - B to Wong Tai Sin Station - B1.
To Avenue of Star, you can take metro from Mongkok station to Tsim Sha Tsui and then walk there.
To Ngong Ping 360 and the Giant Buddha, you can take MTR from Mongkok station to Tung Chung Station, then walk there.
To Macau, you can take ferry from China Ferry Terminal, Tsim Sha Tsui. It is easy to go to Zhuhai from Macau via Gongbei Border.
For shopping, you should not miss the temple street and the Central area.