Hong Kong is easy to explore and surprisingly varied. The MTR, buses, and ferries connect the main attractions without much effort, and the dense geography means you can pack a lot into a short visit.
The obvious starting points are Victoria Peak for the skyline view and the Star Ferry crossing for the harbour perspective. The Temple Street Night Market in Yau Ma Tei is worth an evening, and the Tian Tan Buddha on Lantau makes for an excellent half-day trip. Ocean Park suits families and anyone who wants a full day of rides, animals, and spectacle.
For something more active, Dragon's Back Trail on the southeast of Hong Kong Island is one of the best urban hikes in Asia — three hours along a ridge with sea views on both sides, finishing at Big Wave Bay beach. The government parks in the New Territories offer longer hiking routes for those with more time.
The Sai Kung peninsula in the eastern New Territories deserves a mention: take the ferry to one of the uninhabited islands for swimming, or hire a sampan from the village pier. The Sha Tin Racecourse, one of the world's largest, hosts meetings on Saturday and Sunday from September to June — worth going if you want to see where Hong Kong's gambling enthusiasm gets channelled in public.