Do I need specific travel plans to apply for ESTA?

You do not need specific travel plans when you are applying for an ESTA, you just need to fill in the address where you will be staying. If you’re travelling around the U.S. don’t worry about it – you can always just write the first place you’re staying at as a point of reference. If you haven’t made any concrete plans just yet as your trip is a little short notice, don’t worry about that either, you can list ‘unknown’ as your first point of address, and then that can be edited after 24 hours once you have planned out your trip a little more. In fact, the address of your stay is one of the few things you can edit out after you’ve submitted your application for ESTA, so there’s no need to worry, you don’t need to provide your entire itinerary if you are planning a road trip or if your trip isn’t fully planned out yet.
However, what you will definitely need to have planned and prepared is your return ticket. Remember that the ESTA authorisation is only valid for visits of up to 90 days at a time, so you will need to leave the U.S. before the allotted time has elapsed, as should be shown on your ticket. Also, of course, your chosen travel company or airline will likely ask you for your return ticket before boarding! So make sure you have that prepared, as your return ticket is tangible proof that you’re not going to overstay the 90 day limit for ESTA holders.
There can be some serious consequences if you overstay the 90 days. If you overstay the Visa Waiver program - that is for more than 180 days, but for less than a year, you can be banned from entering the U.S. for a period of up to 3 years. If you overstay for more than a year, then you can get banned from entering the U.S. for up to 10 years. Apart from these, bear in mind that if you’re caught you will be deported from the country. So, it’s important to stay within the 90 day time limit, especially if you plan on applying for ESTA in the future.