While I did not see everything in Singapore, in this video I go over the things that one should definitely see/do while visiting Singapore for just a few days!
Of the many attractions available, one should definitely visit the Singapore Botanic Gardens as well as the National Orchid Garden. I found that you could spend an entire day just walking around and looking at all the tropical plants they have growing there (I did!).
Additionally, visitors should also see the Gardens by the Bay as well as the OCBC skyway to see the SuperTrees (honestly though why are they “SuperTrees”?). While in the area you should also make your way across to the Marina Bay Sands Hotel where you can take the elevator to the rooftop SkyPark (unless of course you are lucky enough to be staying at the hotel, in which case you can access the infinity pool).
Next, heading down to Sentosa Island for a day can provide access to beaches (although the views are not spectacular because of the numerous oil tankers and container ships moored offshore). You can also visit Universal Studios and the Singapore aquarium at Sentosa. Just be warned that Sentosa is one of the more touristy areas and may not be too exciting if you are not in to that type of stuff.
If you are interested in art the National Gallery is a must see as well! Also, make sure you visit the supreme court next door to learn about how the legal system works in Singapore.
Finally, if you are flying out of Changi Airport you must spend at least a couple hours exploring the airport (after all it has been rated the best airport in the world for 5 years in a row). Here you can visit the rooftop sunflower garden, the butterfly garden, relax by watching a movie at the movie theater, cool off at the swimming pool, or enjoy the greenery in the bathrooms and throughout the terminals. Overall, no other airport in the world even comes close to the quality of Changi Airport.
Of course, there are so many other places to visit and explore while in Singapore, but unfortunately I was only able to do so much while there (the jet lag from the 13 hour time change also made me exhausted). 3 days should be plenty of time to see the main attractions and try some good food at the Hawker Centers throughout the city.
Let me know how you would spend 3 days Singapore!
If you want to watch my review of China Eastern Airlines, the airline I flew from Chicago to Singapore, click here: https://youtu.be/LTEl7zr_Lbo