Marina Bay and the CBD area offer the most spectacular views and easy access to major sights but command premium prices. Orchard Road hotels are central for shopping. For more character, try boutique hotels in Chinatown, Keong Saik Road, or Tiong Bahru — a hip neighborhood of 1930s art-deco apartments converted to cafes and restaurants.
Singapore is an expensive city — even budget hotels rarely fall below $80-100/night. Consider Sentosa's resort hotels for beach access. The MRT is so efficient and inexpensive that location matters less than in other cities.