Beaches:
Big Wave Bay Beach
This is probably the nicest beach on Hong Kong Island. Fine white sand, a good mixture of locals and expats and a simple but good beach bar (not so cheap though). You can rent umbrellas and surf boards here.
Shek O Beach
Also a nice beach with a cool beach bar. Next door to Big Wave Bay.
St. Stephen's Beach
Good alternative to Stanley's main beach, usually less crowded. Some trees for those who search the shade and a local style snack bar.
South Bay Beach
Lots of expats here. We didn't like the atmosphere. Too many tossers. Also some trees and a snack bar. But the sand is less fine with lots of pebbles.
Repulse Bay Beach
Spacious beach but the busloads of mainland tourists which cover the beach are annoying unless you like being photographed every 5 minutes or so...
Hiking:
Hong Kong has an amazing country side. There are four main trails with different levels of diffilculty. The best is to buy a hiker's guide in one of the book shops (e.g. The serious hiker's guide to Hong Kong, available at Dymocks). But bear in mind that even for a fit person the trails are sometimes quite strenuous.
1) Hong Kong Trail (Tai Tam Country Park & Peak )
http://en.wikipedia.org/wiki/Hong_Kong_Trail
2) MacLehose Trail (Sai Kung & Tuen Mun)
http://en.wikipedia.org/wiki/MacLehose_Trail
3) Wilson Trail (Stanley & New Territories)
http://en.wikipedia.org/wiki/Wilson_Trail
4) Lantau Trail (Lantau)
http://en.wikipedia.org/wiki/Lantau_Trail
Sports:
Dragonboat
The Tuen Ng festival in May or June is usually the venue for the Stanley dragonboat festival. It's great fun.
http://www.dragonboat.org.hk/en/heritage/special.html
Kayaking & Sailing
There are several watersports centres throughout HK where you can attend courses and rent equipment.
http://www.lcsd.gov.hk/watersport/en/index.php
Outdoor