What if the travelling salesman travelled by plane?
I suggest you read more about the Traveling Salesman Problem.  All of your questions are answered in other standard references (such as the Wikipedia link I gave).  No, the greedy algorithm is not optimal. You may be interested in the Euclidean TSP, which remains NP-hard.  The greedy algorithm is not optimal for that case, either.  No efficient algorithm is known that can always find the optimal solution, though there are algorithms that may be useful in practice.