This is enough to get what I wanted:
Using the HttpGet, Client and Response, I manage to get a server's current time from the response Date Header. I can call this all the times I want and will get confident responses (Google is almost 100% available and I can trust on getting correct Date and Time)
try{
HttpClient httpclient = new DefaultHttpClient();
HttpResponse response = httpclient.execute(new HttpGet("https://google.com/"));
StatusLine statusLine = response.getStatusLine();
if(statusLine.getStatusCode() == HttpStatus.SC_OK){
String dateStr = response.getFirstHeader("Date").getValue();
//Here I do something with the Date String
System.out.println(dateStr);
} else{
//Closes the connection.
response.getEntity().getContent().close();
throw new IOException(statusLine.getReasonPhrase());
}
}catch (ClientProtocolException e) {
Log.d("Response", e.getMessage());
}catch (IOException e) {
Log.d("Response", e.getMessage());
}