The code you are doing now:
currentTimeTextBlock.Text = DateTime.Today.ToShortDateString();
That will set the current date by the phone's clock, and format it with the user's culture settings. This is probably the best thing to do.
Chances are that the user will probably have set their time zone on their phone appropriately. The date and time settings on Windows Phone 8 look like this:
The screen on the right is what it looks like if you change "Set automatically" to "Off". Most users will keep this on. Their phone will automatically update it's time and time zone based on the location.
If they were for some reason to manually set the time zone, then not only would your application be off, but so would everything else on the phone. So I wouldn't try to compensate for that. I know if I were traveling to Russia and my phone didn't update it's time zone, that's probably one of the first things I would do when getting off the plane.