The backup's are located here...
(Mac) ~/Library/Application Support/MobileSync/Backup
(Win Vista) C:\Users\UserName\AppData\Roaming\Apple Computer\MobileSync\Backup
(Win 7) C:\Users\UserName\AppData\Roaming\Apple Computer\MobileSync\Backup
(Win XP) Documents and Settings\USERNAME\Application Data\Apple Computer\MobileSync\Backup
If you are moving to another machine, you will need to move your entire iTunes media library before your first sync, or you will wipe your phone. Moving the backup wont do wont do you any good, its the library that you need to be concerned with.
There are several ways to move your media, between the machines...
1) Copy your entire media library to an external.
2) If your media is "purchased", connect you phone to the new machine, select your device in the left pane, and select "Transfer Purchases".
3) If you have a home wifi network, you can set up "Home Sharing" in iTunes between the two computers (very easy to do, and takes less than a minute), and import the media from one machine to the other.
If you need any more help, PM me or post back here....