Singapore is big on food, so it can probably be covered depending on your preferences. Personally, I'd recommend going for a range from hawker markets to high-end. Booking is important for some higher-end or popular ones, so if you want to go somewhere specific, do that early. Arab Street/Haji Lane, Chinatown and Little India all offer incredible food and are good to walk around.
To be honest, Singapore is pretty small - especially as you're likely to stay fairly centrally - so for first-time tourists, I honestly recommend the open-top buses on your first day. You can view everywhere quickly and then plan the rest of your time from that, and after that, the local MTR and buses are very easy to work out.
Touristy things I've recommended to visitors; the Asian Civilisation Museum is small, central and interesting so if you only do one museum, I'd recommend this one. Gardens by the Bay are beautiful, as are the Botanic Gardens - both enjoyable even if you're not a big gardener. If you like exploring neighbourhoods outside Chinatown and Little India, I'd suggest Joo Chiat.
There's quite a few Asia based MNetters so say what your preferences are and pretty sure there will be some good recommendations