Other than the initial setup, will I need iTunes from a different computer for any reason?
You do NOT need a computer for the initial setup either, if it is running IOS5.
In general iOS devices work without any computer once they are activated. And usually the shops selling those devices offer you to activate them.
Once your iPad is running iOS 5 you can even perform software updates without a computer and backups to the iCloud.
* Although one has to mention that there are limitations for restoring content such as only content (Apps, books, music, ...) available in the iTunes/Apps/iBook store can be restored. For now iCloud also requires a WiFi connection.
You will need computer to upgrade ipad OS, to make backups