Healthcare especially is never free. You're paying for it with taxes or with insurance (or both). If you're paying for it with taxes and tax rates are low, there's a chance costs of living are very high (Singapore, Switzerland) or that the quality of the healthcare isn't very good.
And free healthcare is rarely entirely free all the time. Exceptions and limitations may apply. In some cases, the free healthcare is only for citizens or permanent residents (not new arrivals).
So depending on how you define free healthcare and how you define low tax, a few places come to mind — Cyprus, Hong Kong, Mauritius, Costa Rica, Saudi Arabia, Singapore, Switzerland, Georgia, UAE, Bahamas, and Uruguay.
But each one has its caveats.
I'm not aware of any country that has totally free transport. Some cities here and there do (for all or only for certain groups like residents/citizens). I can't think of any that are located in territories that also have low/no tax and free or nearly free healthcare, though.
It's almost as if governments need other sources of revenue to provide these things for free.