Well, I have some favourite apps that I always use but they are not necessarily SGS2+ specific.
- Android System Info - Nice and easy overview of your battery, space and ram usage and more.
- Google Authenticator - Required for 2-factor protection on your Google account.
- Battery Monitor Widget - Useful for keeping an eye on your battery usage and charge history.
- DiskUsage - Give you an easy to read graphical representation of what's using all your precious storage space, has root features also.
- EBookDroid - PDF and e-book reader.
- ES File Explorer - For moving files about, with LAN/WAN/Cloud support and root features.
- GPS Test - Excellent tool for displaying all sorts of information about your GPS signal.
- KeePassDroid - Android implementation of KeePass, an open source password manager.