You can see what others have to say about the big museums and tourist sites. Everyone has their favorites. Here's my take from my time living in S'pore:
Gardens by the Bay - the evening SuperGrove Tree show is unique. You can always return there just for the show. Daylight will give a better sense of the gardens. Don't miss the domes. https://www.gardensbythebay.com.sg/en/things-to-do/calendar-of-events/garden-rhapsody.html
There is also Spectra for evening light show:
https://www.marinabaysands.com/attractions/spectra.html
The "big" Musuems. (I have not researched for any current closings or on-going reno's):
National Gallery - art museum in the former Supreme Court and City Hall buildings. Galleries are good, rehab of former civic buildings fascinating. Might be worth a tour (free) if very interested. They used to have some focusing on the rehab and others on the art.
National Museum of Singapore - very good if interested in history of Singapore. Easy to self-guide.
Asian Civilizations Museum - heritage of various ethnic groups comprising Singapore. Good museum, self-explore. I think I would pick the National Museum if time for only one of these. Asian Civilizations is good, but National Museum will focus on Singapore and its development. Traveling on to other areas of Asia may cover some of what this museum does. Excellent exhibit of Maritime Trade with a Tang era shipwreck showing its cargo if this is an interest for anyone.
Several excellent "specialist" museums if interested in WWII or ethnic areas. I have not researched these to see the current status of openings, but to give you an idea:
ethnic - Peranakan Museum, Malay Heritage Centre, Indian Heritage Centre, Chinatown Heritage Museum
WWII - Changi Chapel & Museum, Former Ford Factory, BattleBox at Fort Canning, there are more - many are small and slightly out of the way, but excellent
Comments on the two Gardens options from my personal perspective. If time for only one, I couldn't advise which to choose - too personal a choice:
Botanic Garden and National Orchid Garden are incredible gardens. Traditional presentation of botanic gardens with lots more than many botanic gardens elsewhere. My favorite Botanic Garden in the world - for reference, London's Kew Gardens comes second for me.
Gardens by the Bay - unique (at least in my experience) The domes are great fun, the gardens extensive, SuperGrove unique. Many would consider an S'pore must-see
I am homesick!! I'm interested in what Simon has to say as a current resident!!!