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. then you can just write the first place you’re staying at as a point of reference. If you haven’t made your plans just yet as your trip is a little short notice, you can list ‘unknown’ as your first point of address, and then that can be edited after 24 hours once you have had time to plan out your trip. The address of your stay is one of the few things you can edit after you’ve submitted your application for ESTA, so it is not a problem if you do not have those details when you submit your application. 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 restricted time period has elapsed, as should be shown on your ticket. Also, your 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 planning to overstay the 90 day limit for ESTA holders.
There can be some serious consequences if you overstay the 90 consecutive days or if you overstay the Visa Waiver program annual limit - that is for more than 180 days in one 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. In addition to these bans, if you’re caught overstaying the limit 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.