Transportation in Singapore is very easy to get around, and using the MRT (Subway) and Buses will be the most economical. I recommend buying an EZ-Link card. They cost $12 SGD ($5 of which is card cost and $7 is for paying fares) You can buy them at most MTR stations and they are easy to top up in $10 increments at MRT station machines or 7-Elevens. While this might not sound practical, you are actually getting a discount on the fares, rather than buying each fare individually.
Some people may recommend buying a Singapore Tourist Card which gives unlimited rides for $10 per day, but that also requires an additional $10 deposit (You can get the deposit back when returning the card) While this may sound like a good deal, it would take around five rides per 24 hours to break even on the card. So this might be a better option if you are trying to pack in 3 or more attractions per day. But I only ended up taking transit 2-4 times per day at most, so the EZ-Link card was actually cheaper for me because the card is not set to a time limit. They do offer a 2 day and 3 day pass that are slightly cheaper, but I still think you would save by getting an Ez-Link card and just topping up when needed.
Taxi cost are also very affordable with basic fare costing around $4 SGD ($2.90 USD) and around $0.70 SGD ($0.51 USD) per km. From Changi Airport to the Center City should cost around $20-$35 SGD ($14.50-25 USD).
Grab is the ride-hailing app of choice for many Singaporeans, and also popular in many other Southeast Asian countries. If your familiar with Uber or Lyft you will feel right at home using this app.
E-Scooters can be rented around the Marina Bay areas of Singapore and cost a couple of Singapore dollars per hour. They also have a rideshare e-scooter you can rent using an app called Neuron. Not only are these an economical way of getting around the Marina Bay area, they also cover a lot of ground quickly and are quite fun.
