function save_options() {
      var color = document.getElementById('color').value;
      chrome.storage.sync.set({
        favoriteColor: color
      }, function() {
        console.log("Color saved");
      });
    }

var color = null;
    chrome.storage.sync.get('favoriteColor', function(item){
        color = item.favoriteColor;
        //alert(color); //Here works;
});

alert(color); // here doesn't work

var color = null;
        chrome.storage.sync.get('favoriteColor', function(item){
            color = item.favoriteColor;
            alertColor(color);
    });

    function alertColor(color){
        alert(color);
    }