Three options for you:
1. Using just JavaScript's Date
object (no libraries):
My previous answer for #1 was wrong (it added 24 hours, failing to account for transitions to and from daylight saving time; Clever Human pointed out that it would fail with November 7, 2010 in the Eastern timezone). Instead, Jigar's answer is the correct way to do this without a library:
// To do it in local time
var tomorrow = new Date();
tomorrow.setDate(tomorrow.getDate() + 1);
// To do it in UTC
var tomorrow = new Date();
tomorrow.setUTCDate(tomorrow.getUTCDate() + 1);
This works even for the last day of a month (or year), because the JavaScript date object is smart about rollover:
// (local time)
var lastDayOf2015 = new Date(2015, 11, 31);
console.log("Last day of 2015: " + lastDayOf2015.toISOString());
var nextDay = new Date(+lastDayOf2015);
var dateValue = nextDay.getDate() + 1;
console.log("Setting the 'date' part to " + dateValue);
nextDay.setDate(dateValue);
console.log("Resulting date: " + nextDay.toISOString());
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