Issue 

The problem we have is we might have one item, built in China, and if it's stocked here, our cost is higher than if it is stocked in our China plant.

I was looking at the stockkeeping units to hold a separate cost for this one item in two different locations.  Though in testing it, what I've found is that the average price changes per item, rather than per location (I've adjusted my setup in inventory to do the average cost cal. type to per item/location/variant, rather than just item.)

Is this the way it is supposed to work, with avg. cost always per item?  The setup seems to suggest otherwise.
Solution

This is how the cost by location works in Navision. Say inventory is stocked at China and Canada

After Item 'A' is manufactured in China, Average Cost = $10/Unit
When this Item 'A' is transferred from China to Canada, the Unit Cost of the item still stays at $10, as there is no other cost associated with the item.

Typically, the cost of an item would differ from one stocking location to another due to additional charges like, Freight, Customs Duty, etc.

For Navision to maintain different costs at China and Canada for the same item, these additional costs incurred in the transportation of the item have to be assigned/apportioned to the item. This is done in Navision using "Item Charges." Once these charges have been assigned to the items which were received in Canada, you will see:

Unit Cost in China = $10
Unit Cost in Canada = $12, where $2 is the additional cost per unit incurred in the transfer of the item from China to Canada.

The above process would have to be followed in order for the system to maintain two different costs for the same item by location, along with the Setup Parameters in the inventory setup as you described.