Given that Tableau will not be able to decide which labels would be kept so that the map is the most visually pleasing, this should be done partially manually.
Just place Region on Label first. Then, CTRL + click on each county where you don't want the labels shown. You could casually do it the first time since you will be able to add on to this list later.
After you have multi-selected all these counties, right-click on one county, click Create Set..., and click OK.
Now, create a calculated field that goes:
if not [Set 1] then [Region] end
And replace Region with this calculation on the Marks card.
You can now add on whatever counties you want to exclude further to Set 1, and their labels won't show.
See my follow-up below.
if you have Tableau 10, you could create custom terriitories, then you have 1 label per "region"
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Please ignore my initial post, and consider this three-step approach:
Right-click on Region, go to Geographic role > Create from... > County.
Place the hierarchy on Label, and drill-down that hierarchy using the minus sign next to Region.
That's perfect, thank you! I was originally trying to figure out how to assign geographical coordinates to my region variable and I couldn't figure it out. I am not surprised that the solution was along these lines. Much appreciation!
Cambria, please mark my answer as correct so that:
1. Others will be able to see my answer more easily, and
2. I score precious Internet points.