What parts of Machiavelli's advice in The Prince would still apply in the modern world?
Most of Machiavelli's advice would not apply at all to the modern world because it is aimed at autocratic rulers. Modern democratic rulers could not gain much by reading this book. However, there are still rulers in parts of the world who might be helped by the book. This would be true of the rulers of China, for example, who seem to think that it is better for them to be feared by their subjects than it would be for them to be loved.
There are other, lesser known, parts of Machiavelli's advice that would be applicable even to democracies. For example, Machiavelli says that leaders should be ready to change their tactics and ideas when needed. He says that things sometimes happen that make it necessary to abandon preconceived plans. This is surely just as true today was it was in Machiavelli's time.