[Neor]

А вот так?

cityName.addEventListener('keypress', function(e) {
  if (e.keyCode == ENTER_KEY_CODE) {
    var url = creatingUrl(cityName);
    weather = query(url);
    console.log(weather); //undefined
  }
});

function query(theUrl) {
  xhr.open('GET', theUrl);
  xhr.send();
  xhr.addEventListener('readystatechange', function() {
    if (xhr.readyState != xhr.DONE) {
      return;
    }
    if (xhr.status != 200) {
      console.log('Error? Error!');
    } else {
      var serverAnswer = JSON.parse(xhr.responseText);
      console.log(serverAnswer);
      OtherWeatherData.style.display = 'block';
      requestAccepted(serverAnswer);
      return serverAnswer;
    }
  })
}