Singapore is a beautiful city. It's known for its harsh laws on what many consider minor infractions like littering, so it's pretty clean. and the city has worked hard to build a beautiful skyline. The unbelievably popular area around the Merlion is no different.
Note the pedestrian bridge being built between the Esplanade and the Merlion (to the right out of frame). By now, that bridge should be open, making for a much more peaceful stroll across the mouth of the Singapore River.
Anyway, the Merlion statue and waterfront area is a short walk from the Raffles Place subway station. Marina Bay Sands is best accessed via Bayfront Station or by walking from the Merlion. The Esplanade center and park are across the river to the north; Esplanade or Promenade stations are both close by. For architecture or walking fans, that whole area has a lot of promise.
The Merlion is very popular and a key stop for all tour groups, so be prepared. Maybe visiting in the afternoon will have lesser crowds; note that the statue is also lit at night and is worth seeing then too.