You can do this in native JavaScript. You'll have to parse your data into correct CSV format as so (assuming you are using an array of arrays for your data as you have described in the question):

const rows = [
    ["name1", "city1", "some other info"],
    ["name2", "city2", "more info"]
];

let csvContent = "data:text/csv;charset=utf-8,";

rows.forEach(function(rowArray) {
    let row = rowArray.join(",");
    csvContent += row + "\r\n";
});

or the shorter way (using arrow functions):

const rows = [
    ["name1", "city1", "some other info"],
    ["name2", "city2", "more info"]
];

let csvContent = "data:text/csv;charset=utf-8," 
    + rows.map(e => e.join(",")).join("\n");

Then you can use JavaScript's window.open and encodeURI functions to download the CSV file like so:

var encodedUri = encodeURI(csvContent);
window.open(encodedUri);

Edit:

var encodedUri = encodeURI(csvContent);
var link = document.createElement("a");
link.setAttribute("href", encodedUri);
link.setAttribute("download", "my_data.csv");
document.body.appendChild(link); // Required for FF

link.click(); // This will download the data file named "my_data.csv".

Based on the answers above I created this function that I have tested on IE 11, Chrome 36 and Firefox 29

function exportToCsv(filename, rows) {
    var processRow = function (row) {
        var finalVal = '';
        for (var j = 0; j < row.length; j++) {
            var innerValue = row[j] === null ? '' : row[j].toString();
            if (row[j] instanceof Date) {
                innerValue = row[j].toLocaleString();
            };
            var result = innerValue.replace(/"/g, '""');
            if (result.search(/("|,|\n)/g) >= 0)
                result = '"' + result + '"';
            if (j > 0)
                finalVal += ',';
            finalVal += result;
        }
        return finalVal + '\n';
    };

    var csvFile = '';
    for (var i = 0; i < rows.length; i++) {
        csvFile += processRow(rows[i]);
    }

    var blob = new Blob([csvFile], { type: 'text/csv;charset=utf-8;' });
    if (navigator.msSaveBlob) { // IE 10+
        navigator.msSaveBlob(blob, filename);
    } else {
        var link = document.createElement("a");
        if (link.download !== undefined) { // feature detection
            // Browsers that support HTML5 download attribute
            var url = URL.createObjectURL(blob);
            link.setAttribute("href", url);
            link.setAttribute("download", filename);
            link.style.visibility = 'hidden';
            document.body.appendChild(link);
            link.click();
            document.body.removeChild(link);
        }
    }
}

For example: https://jsfiddle.net/jossef/m3rrLzk0/

This solution should work with Internet Explorer 10+, Edge, old and new versions of Chrome, FireFox, Safari, ++

The accepted answer won't work with IE and Safari.

// Example data given in question text
var data = [
  ['name1', 'city1', 'some other info'],
  ['name2', 'city2', 'more info']
];

// Building the CSV from the Data two-dimensional array
// Each column is separated by ";" and new line "\n" for next row
var csvContent = '';
data.forEach(function(infoArray, index) {
  dataString = infoArray.join(';');
  csvContent += index < data.length ? dataString + '\n' : dataString;
});

// The download function takes a CSV string, the filename and mimeType as parameters
// Scroll/look down at the bottom of this snippet to see how download is called
var download = function(content, fileName, mimeType) {
  var a = document.createElement('a');
  mimeType = mimeType || 'application/octet-stream';

  if (navigator.msSaveBlob) { // IE10
    navigator.msSaveBlob(new Blob([content], {
      type: mimeType
    }), fileName);
  } else if (URL && 'download' in a) { //html5 A[download]
    a.href = URL.createObjectURL(new Blob([content], {
      type: mimeType
    }));
    a.setAttribute('download', fileName);
    document.body.appendChild(a);
    a.click();
    document.body.removeChild(a);
  } else {
    location.href = 'data:application/octet-stream,' + encodeURIComponent(content); // only this mime type is supported
  }
}

download(csvContent, 'dowload.csv', 'text/csv;encoding:utf-8');

Running the code snippet will download the mock data as csv

Credits to dandavis https://stackoverflow.com/a/16377813/1350598