Every mapping website I know of - and I think I've tried them all - requires that you pick your prospective destinations one at a time and in the sequence you want to use. I don't know of any that let you specify several destinations and then grinds out the optimum route to connect them all. Sounds like the kind of thing that a trucking company or delivery service would use. I know UPS uses something like it, and it's proprietary and closely-guarded.
I use DeLorme Street Atlas USA, which lets you pick starting and ending points and then add in stops in between, and it kind of tries to do what you want, but doesn't succeed.
al