Extract App Data from Nandroid / CWM Backup
In addition to the well-known Titanium Backup app (for which you must purchase the Pro key to unlock the CWM/TWRP nandroid backup support), there is another app now: Nandroid Manager, which according to its description can restore apps from nandroid backups even with the free version (there is a Pro key too, but it is required if you want to restore special data such as Wi-Fi access points, Bluetooth data, user dictionary and browser data). However, I did not try using this app.