Yes, the location order can be rearranged.
1. First, tap the menu in the upper Left.
2. Select the Pencil icon to access the Edit Locations screen.
3. On the left hand side of each location you will see a drag area.
3a. Long-press on that area and drag to rearrange the locations in the list.
Note: "My Location" will always remain the first location in the list.