No, I didn't mean the desktop of the PC, I meant my desktop (as opposed to laptop) PC. Itunes puts the music, the pictures, the apps and the rest where I tell it.
The issue was that I'd been syncing the iPhone to the laptop computer, but for various reasons changed it to sync to the desktop computer. That was when I discovered that the desktop PC wouldn't back up the iPhone properly. Eventually I solved that with the "repair program" features of Windows 7.
IO540
Backups only "appear" when the relevant device is connected. Plug in your iPhone, start iTunes, then when the iPhone appears in the devices list, click Edit - Preferences - Devices. You should see "IO540's iPhone" and a date and time in there.
It won't back up the music on the device, because that's in the iTunes library on the PC, but it will back up everything else. If your iPhone glitches, or you buy a new one, you can restore all that stuff to the new one. It even keeps text messages, call history, settings, photos and so on.
If you feel the need, and if other folks have access to your PC, you can even encrypt the backups.
I've never bothered to look to see where on the PC the iPhone backups go. The way mine is set up, it keeps only the most recent. I've also not bothered to look for a way to keep several. Most of the stuff on the iPhone is duplicated elsewhere in my system anyway.