Vue.js filtering on array

You weren't too far off.

For your searchEvents filter, you just needed to add the tag filter. Here's how you might do that.

searchevents: function(){
    let result = this.events
    if (!this.filterValue)
      return result

    const filterValue = this.filterValue.toLowerCase()

    const filter = event => 
        event.name.toLowerCase().includes(filterValue) ||
        event.state.toLowerCase().includes(filterValue) ||
        event.tags.some(tag => tag.toLowerCase().includes(filterValue))

    return result.filter(filter)
}

Array.some() is a standard array method that returns true if any element of the array passes your test.

searchevents2: function(){
    const searchRegex = new RegExp(this.filterValue,'i')
    return this.events.filter(event => 
      !this.filterValue || searchRegex.test(event.name) || searchRegex.test(event.state))
}

With searchEvents2 you really only left an errant self in there. Either you needed to set self before you executed the filter, or, as I have done here, turned it into an arrow function.

Example.

const app = new Vue ({
  el: '#app',
  data: {
    search: '',
    userList: [
      {
        id: 1,
        name: "Prem"
      },
      {
        id: 1,
        name: "Chandu"
      },
      {
        id: 1,
        name: "Shravya"
      }
    ]
  },
  computed: {
    filteredAndSorted(){
     // function to compare names
     function compare(a, b) {
       if (a.name < b.name) return -1;
       if (a.name > b.name) return 1;
       return 0;
     }
      
     return this.userList.filter(user => {
        return user.name.toLowerCase().includes(this.search.toLowerCase())
     }).sort(compare)
    }
  }
})

<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.4.2/vue.js"></script>
<div id="app">
  <div class="search-wrapper">
    <input type="text" v-model="search" placeholder="Search title.."/>
        <label>Search Users:</label>
  </div>
  <ul>
    <li v-for="user in filteredAndSorted">{{user.name}}</li>
  </ul>
</div>