Methods can't be called on a null reference; it looks like getChildElement('State',null) is returning a null value, so you should check that first:
Dom.XmlNode stateNode = xroot.getChildElement('State',null);
if(stateNode != null && stateNode.getText() != null) {
Based on the additional comment, it looks like you need to read the ZipCode node to get to the State:
Dom.XmlNode zipNode = xroot.getChildElement('ZipCode',null),
stateNode = zipNode == null? null: zipNode.getgetChildElement('State',null);
if(stateNode != null && stateNode.getText() != null) {