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

document.getElementById('input').addEventListener('keyup', filter());

function filter() {
	var cities = document.querySelectorAll('#list > li');
  
  return function(e) {
  	cities.forEach(function(city) {
    	var regexp = new RegExp('^' + e.currentTarget.value, 'i');
      var value = city.children[0].textContent;
      !regexp.test(value) ? city.style.display = 'none' : city.style.display = '';
    })
  }
}