Вы можете отсортировать массив dates
по абсолютной разнице между текущей датой и извлечь первый элемент:
var dates = [
'Aug 18, 2018 03:24:00',
'August 19, 2018 03:24:00',
'September 17, 2018 03:24:00',
'September 14, 2018 03:24:00',
'August 18, 2018 03:24:00',
'July 16, 2018 03:24:00',
'July 15, 2018 03:24:00',
'December 15, 2018 03:24:00',
'July 13, 2018 03:24:00',
];
var now = new Date();
var [ closest ] = dates.sort((a,b) => {
const [aDate, bDate] = [a,b].map(d => Math.abs(new Date(d) - now));
return aDate - bDate;
});
console.log(closest);