I tried downloading StarCraft II via the provided Blizzard downloader app, but pointed it to a partition that was formatted FAT32. Since the file is larger than FAT32 can hold (~4GB) the download failed. The downloader does not provide you with a way of switching the download location after you run it the first time; to do so, you need to edit the Windows registry. Here’s how:

Click your Windows “Start” button and select “Run”, or hold down the “Windows Key” and press “R”.
Enter “regedit” in the “Open:” dialogue box and press OK.
Press “Ctrl” and “F” to open the Find dialogue.
Enter “Blizzard Entertainment”. It should display a folder on the left entitled “Blizzard Entertainment”. Expand this folder by clicking the “+” to the left of it. You should see a “Downloader” folder. Expand this too. There should be a key with some random string of alphanumerics. Click on that.
In the right pane you should see a key that titled “Path”. Right click on that and click “Modify.”
Change the “Value data” to set the location for the download folder and press “OK”. Close RegEdit.
Enjoy!

Standard disclaimer: when mucking about in your registry, be careful, as you can bork Windows.