JSFiddle - React, Tailwind, and code Playground

HTML

<input type="text" id="input" placeholder="Введите город">

<ul id="list">
  <li><a href="#">Абакан</a></li>
  <li><a href="#">Агидель</a></li>

  <li><a href="#">Кемерово</a></li>
  <li><a href="#">Киров</a></li>
  
  <li><a href="#">Москва</a></li>
  <li><a href="#">Мытищи</a></li>
</ul>

JavaScript

var input = document.getElementById('input')[0];
input.addEventListener('onkeyup', function() {
  citiesFilter();
});

function citiesFilter() {

		var filter = input.value.toUpperCase(),
    		ul = document.getElementById("list"),
    		li = ul.getElementsByTagName("li");
        
    var i, a;    
    for (i = 0; i < li.length; i++) {
        var a = li[i].getElementsByTagName("a")[0];
        if (a.innerHTML.toUpperCase().indexOf(filter) > -1) {
            li[i].style.display = "";
        } else {
            li[i].style.display = "none";

        }
    }
    
}