Greatest among any other town is impossible. That is a comparison with only one other town, and one town (or population) cannot be "among" only one other.
Your first suggestion, greater than any other town, is acceptable, but a little loose; your second is even better, because it compares populations instead of comparing a population to a town: it answers the question "Which of these two populations is greater?"
Those constructions compare Tokyo's population to that of each other town, one by one. You may employ the superlative greatest only if you compare Tokyo's population to those of all the towns in a group of at least three towns. When performing a comparison of this sort, Tokyo itself must be included in the group whose populations are compared, so you may not use the term other.
This is a little trickier to construct with precision, because when you refer to the multiple populations you must be careful to exclude the possibility that you are comparing Tokyo's population to the sum of the populations of the other towns. You may accomplish this by "detaching" each town from its population and asking a slightly different question: "Which town has the greatest population?"
Among all towns in the world, Tokyo has the greatest population.
Tokyo has the greatest population of any town in the world.