When I synced my old ipod with my new iMac I no longer have my old playlists. (probably did not do it correctly). I have a back-up of my old iMac on an external hard drive, is there any way I can restore my old playlists?
Connect the external with the backup of your old iMac to the new iMac.
If you used Time Machine, you'll need to use Time Machine on the iMac to restore the old iTunes library last used on your old iMac.
If you just manually transferred documents, photos and media (music and videos) from hard drive to hard drive, you'll just need to drag and drop from the external to your new iMac these files and folders.