[destus]

Blondinka,
JSON структура неправильная. Должно быть так

cityList.json

[
  {"_id":707860,"name":"Hurzuf","country":"UA","coord":{"lon":34.283333,"lat":44.549999}},
  {"_id":519188,"name":"Novinki","country":"RU","coord":{"lon":37.666668,"lat":55.683334}},
  {"_id":1283378,"name":"Gorkhā","country":"NP","coord":{"lon":84.633331,"lat":28}},
  {"_id":1270260,"name":"State of Haryāna","country":"IN","coord":{"lon":76,"lat":29}},
  {"_id":708546,"name":"Holubynka","country":"UA","coord":{"lon":33.900002,"lat":44.599998}},
  {"_id":1283710,"name":"Bāgmatī Zone","country":"NP","coord":{"lon":85.416664,"lat":28}},
  {"_id":529334,"name":"Mar’ina Roshcha","country":"RU","coord":{"lon":37.611111,"lat":55.796391}}
]

.js

function get(url) {
    return new Promise(function(resolve, reject) {
        var req = new XMLHttpRequest();
        req.open('GET', url);

        req.onload = function() {
            if (req.status == 200) {
                resolve(JSON.parse(req.response));
            }
            else {
                reject(Error(req.statusText));
            }
        };
        req.onerror = function() {
            reject(Error("Сетевая ошибка"));
        };
        req.send();
    });
}

get('cityList.json').then(function(response) {
    "use strict";
    let findName = 'Hurzuf',
        idx = response.findIndex(obj => Object.is(obj.name, findName));

    alert(idx);
}, function(error) {
    console.error("Не удалось выполнить!", error);
});