How can I transfer iPhone + iPad data to a new computer?
Solution 1:
There's an Apple guide to this process
There's also this guide on HowToGeek.com
Solution 2:
From my experience, unless you use Time Machine or Migration Assistant, it's not that easy task we'd expect it to be. Here's a very complete guide, here's a very simplistic one and here's another one that envolves hacking iTunes library and isn't exactly about just copying.
iTunes is a very messy program and it can easily become hard to keep it clean on just one machine. Transferring it to another machine is adding one more layer of mess.
As last resource, try some third party tool, such as syncopation. I haven't tried any myself, but seems very promising and most of them have free trials.
Solution 3:
Recently dealt with this problem with my parents upgrading from an iPad 2 to an iPad 3.
The iPad 2 was synced to one laptop, the iPad 3 was destined for another. We synced the iPad 3 to a backup of the iPad 2 and then went to plug it into the new laptop. (NOTE: the new laptop had all files from the old library synced via home share first.) iTunes asked whether to leave it alone or erase the iPad and sync. After playing around and much googling we went ahead and tried hitting erase and sync. When you do this, if the two iTunes libraries have the same iTunes account, it will actually make a full backup of the iPad BEFORE it "erases and syncs."
Once it was done, all files were there, even each app's files and settings. (Such as PDFs saved in good reader).