[Vuejs]-Vue.js computed value never run on startup

Computed property is a property which depends on data properties.

In your case it is better IMO to create a data property skin, and a method like setSkin() which initializes the skin data property, and another method saveSkin() to save your property into localStorage.

You then can run setSkin() in mounted() hook.

Template:

new Vue({
  el: '#app',
  data: {
    skin: ''
  },
  methods: {
    setSkin: function() {
      this.skin = ...;
    },
    saveSkin: function() { // call this function when you need to save skin data into localStorage
      window.localStorage.setItem("skin", this.skin);
      ....
    }
  },
  mounted() {
    this.setSkin(); // retrieve skin data from localStorage, etc.
  }
});