PAMJP, here are a couple of areas to possibly consider:
Marina Bay- upmarket shopping, casino (eg Marina Bay Sands, Fullerton, Fullerton Bay.)
City Hall - above MRT station and interconnecting shopping centres (eg Fairmont)
Orchard Road- main street (eg Shangri-La, Mariott Tang Plaza, Hilton, St Regis)
We liked the location of the Fairmont, as it was easy to get around. There is an another hotel literally next door- Swisshotel the Stamford- which may be worth a look.
We were less keen on the Hilton as it was old and Orchard Road can become very crowded and hot, but perhaps an experience that a first-time visitor would not mind.
4/5 star hotels in Singapore are expensive, but like you say, taxis are not, so getting to places is easy.