Application to plan optimal route between multiple cities
score:4
Accepted answer
The problem that you state is known in academia as the Traveling Salesman Problem as pointed out by @ZachLipton.
Googling for that expression in combination with app/website/software gives a few good finds.
As apps I could find e.g. Concorde TSP and Route4Me (no affiliation nor experience).
A nice online tool is Optimap which seems to use Google directions. Here is a random route along the US east coast. You can choose between a roundtrip and or ending up in a different city than where you started from.
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