Any way to get the Spotlight window to show "where" the files are?

no unless you click on "show all" to load the search in another window.

If you're using the Spotlight menu, doesn't it show you the file's path in a tooltip when you hover the mouse over an item?

What I do, though, is just initiate a search in a Finder window, which is much better featured than using the menu.

If you click on show all in spotlight each item has an "i" at the end. Click on this and it will show you the files path. This is better than the hover option because you can always see the link on your screen, instead of remembering it all from when you hoverred over it. It is just as quick as well.

just hover over the search results to reveal the path...

In case you haven't noticed the hover before, I don't think the tooltip appears until spotlight has finished finding results. Otherwise you have to use the big Spotlight windows....

[update] 10.8 Show file Path

In Mountain Lion you can hold down Command +Option to show the file paths of found files.