Turn on the WI-FI connection on your old iPhone and coonect it to power source. Then, tap on Settings > iCloud > Storage & Backup to enable iCloud Backup. By default, it backs up notes, photos, bookmarks, contacts, calenars, etc. Of course you can manually set what to be backup, but make sure that notes is checked!
Now turn on your new iPhone 7, start to set up your new phone, navigate to Restore from iCloud Backup, sign in your iCloud account, then choose backup.