Edit in JSFiddle

<!DOCTYPE html>
<html>
  <head>
    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <link rel="stylesheet" href="https://unpkg.com/[email protected]/dist/leaflet.css">
    <script src="https://unpkg.com/[email protected]/dist/leaflet.js"></script>
  </head>

  <body>
    <div id="map"></div>

  </body>
</html>
#map {
  height: 400px;
}
var mymap = L.map('map');

L.tileLayer('https://cyberjapandata.gsi.go.jp/xyz/std/{z}/{x}/{y}.png', {
  maxZoom: 18,
  attribution: '<a href="https://maps.gsi.go.jp/development/ichiran.html" target="_blank">国土地理院</a>',
}).addTo(mymap);

mymap.setView([37.508106, 139.930239], 15);


var markerIcon = L.icon({
    iconUrl: 'http://www.nowhere.co.jp/blog/wp-content/uploads/2018/07/marker.png', // アイコン画像のURL
 
    iconSize:     [32, 32], // アイコンの大きさ
    iconAnchor:   [16, 32], // 画像内でマーカーの位置を指し示す点の位置
    popupAnchor:  [0, -32]  // ポップアップが出現する位置(iconAnchorからの相対位置)
});

var marker01 = L.marker([37.508106, 139.930239], {icon: markerIcon}).addTo(mymap);
var marker02 = L.marker([37.494833, 139.929750], {icon: markerIcon}).addTo(mymap);

marker01.bindPopup("会津若松駅");
marker02.bindPopup("会津若松市役所");

var route = L.polyline([
    [37.507543, 139.930619],
    [37.507016, 139.932408],
    [37.498371, 139.928649],
    [37.495337, 139.928006],
    [37.495123, 139.929800],
    [37.494833, 139.929750]
], {color: "blue", weight: 6}).addTo(mymap);

route.bindPopup("駅から市役所までの経路");