As invisible has alluded to, the Singapore forum would have some excellent suggestions. As to solo travel, Singapore is one of my favorites because it's so easy to navigate, as a solo traveler. While I've been shown around during my initial visits, in my view, you could more or less see most of Singapore in a day or two. Off the top of my head, the Lion head, that garden, the evening light show (with Star Wars music), hawker stands, Orchard Road stuff, Marina (building with ships on top), Sentosa Island, durian street vendors (if you're into then fruit), Chinatown, pick out some nice restaurants, e.g., Hainan Chicken rice, roast duck, etc.

As a solo traveler, if your budget allows for it, taking taxis and/or Grab is pretty affordable. My last ride from SIN into the city was only about 16 SGD? Beats the subway, in my view.