HDB=housing development board, its a board which does the high
rise apartments or flats which could be 3-4 rooms, + a living room
and kitchen.
When since Singapore is quite small, there is almost always a
coffee-shop, 24hrs 7-11 grocery shops, within the "new town" you
intend to stay in.
Most probably clementi or such.
There are also karaoke, library, sports stadium, swimming pools,
cinemas, theatres, skating rink, science centre, and over services
in the west (where NUS and NTU is).
Have fun. 
Remember to visit iconic places like Sentosa, Bird Park, Ubin, Zoo
(Night Safari), Science Centre and Discovery Centre, Duck Tours,
East Coast Recreational Centre (like surfing, blading, cycling,
bowling, seafood, yatching, canoeing etc).
Some interesting places to window shop includes Orchard area,
Suntec, Chinatown, etc. 
