districts
The best way to explore Hong Kong is to pick a neighborhood and head out.  Most of Hong Kong is serviced via the MTR, hence this categories name, however, there are also quite a few places worth seeing by either bus or ferry.  I've summarized my favorite neighborhoods and what makes them distinct below.

HONG  KONG  ISLAND

CHAI WAN
The far end of the Island Line.
SHAU KEI WAN
Museum of Naval Defense, several small temples, and a bustling meat and vegetable market.
TIN HAU
Nearby Tai Hing is my favorite section of Hong Kong because of the small city block atmosphere.

KOWLOON

KOWLOON CITY
Home to Hong Kong's "Thai Town" and within range of a few worthwhile religious sites.
KWUN TONG
This appears to be an up and coming area - new buildings and a new waterfront promenade
MONG KOK
Holds the Guiness World Record for "Busiest District"...it's pretty busy.
SHAM SHUI PO
Densely populated neighborhood that bursts with activity after working hours.

NEW  TERRITORIES

SHA TIN
Mega "suburb" with a Horse Track, 10,000 Buddhas Monastery, and exposure to Hong Kong daily life.
TAI PO / FANLING
Two large residential areas north of Sha Tin on the Eastern line.  Good food and walled villages.
YUEN LONG
Large district deep in the Northwest Corner of New Territories - a little more lively than Sha Tin and Tai Po.