How do you wait for a Network Stream to have data to read?

You can use the async methods of the NetworkStream and set a ManualResetEvent in the EndReceive method.

// ...
netStream.BeginRead(buffer, offset, callback, state);
// ...

inside the callback method

netStream.EndRead(ar);
netStreamManualResetEvent.Set();

then your code

while (notDone)
{
    WaitHandle.WaitAny(new WaitHandle[] { queue1.HasData, queue2.HasData, netStreamManualResetEvent} );
    // ...
    if (netStream.DataAvailable)
    {
        // make the buffer from the AsyncState in the callback method available here
        // process buffer
    }
}

The simplest way is probably to use an additional thread which reads synchronously and puts extra data onto an extra queue.

Alternatively you could use asynchronous IO, but that's somewhat tricky - and you'd still need to have some additional queue.

Although Socket has a Select() method (and you can get at a socket from a NetworkStream) I don't believe it exposes this functionality in a way which lets you mix it with other kinds of wait handles.