Use migration assistant to move all of your data to your new Mac:
http://support.apple.com/kb/HT4413
App data is store in only two places: on your phone and in your iPhone backup. By design, an iPhone will sync iTunes content with ONE computer at a time. Any attempt to sync with a second computer will result in ALL iTunes content being first erased from your phone & then replaced with the content from the second computer. If you use migration assistant to move all of your data, this won't present a problem since you'll be replacing like content with like content.
To preserve your app data, do this AFTER you move everything to your new computer: First, disable auto-sync under iTunes>Preferences>Devices. Connect your phone, DO NOT SYNC at this point. Right-click the phone in the left device pane and select "Backup". Once complete, right-click again and select "Restore from Backup". Select the backup you just made. If prompted to create another backup first, decline. Follow this by syncing your content back to your phone.
When finished, your phone should look just like it did when you started with all of your app data preserved & you're now syncing to your new computer.