I stucked at the same Point when I recently started to Play around with VS2013 and my first store app. I have not much experience in C#, but I hope what I found out for VB may help you as well.
Youre right, the examples with "System.Net.DNS" don't work for Store-Apps. But after some researches I found the class "Windows.Networking.Connectivity.NetworkInformation.GetHostNames" that can be used to get not only the Host Name but also the IPv4 and v6 addersses.
The following code works fine in Visual Basic
HostNamesObj = Windows.Networking.Connectivity.NetworkInformation.GetHostNames
For Each HostName In HostNamesObj
If HostName.Type = 0 Then
ComputerNames= HostName.ToString
End If
If HostName.Type = 1 Then
IPv4_Output = HostName.ToString
End If
If HostName.Type = 2 Then
IPv6_Output = HostName.ToString
End If
Next
If you succeed to translate this to C#, I would be very happy about your Feedback, because that's the Point where I'm strugling right now. I just realized that C# has a lot in common with VB, but it's much more sensitive regarding the type declaration for variables!
So:
Good luck, RoadrunnerLI