Can I stay in the US for a few days if my ESTA was indicated for transit?

I agree with the other answer that no is a safe answer, but I also believe that you do not need to apply for new ESTA authorization. CBP says

If you obtain a new passport or change your name, gender or country of citizenship, you will be required to apply for a new travel authorization. This is also required if one of your answers to any of the VWP eligibility questions changes. The associated fee of $14 will be charged for each new application.

As far as I understand it, this does not apply to you because the question about whether you're in transit or not is on the "travel information" page, not the "eligibility questions" page.

Furthermore, there's no separate "transit" category of ESTA authorization. Nonimmigrant classes are defined at 8 CFR 214.1, and the only visa waiver categories are WT, for "visa waiver, tourist," and WB, for "visa waiver, business." A person in transit would therefore be admitted in one of those two categories, which both allow a 90-day stay. It would be truly odd for someone to be given trouble because they chose "transit" on the ESTA application.

Another fact in favor of this interpretation is that the US continues to use a (nearly obsolete) definition of transit for C-1 visas whereby a traveler in transit may be admitted for up to 29 days. If you are staying even for a few days days for a long layover, but have no other significant purpose in the US, then your visit really is transit in a real sense. If you decide to remain a few days longer than necessary, then you have an additional purpose as a "visitor for pleasure," but as outlined above that should be fine.

As pointed out by Honorary World Citizen, however, in a comment, the consequences of refused entry are severe, so if the above analysis leaves you uncertain, it's probably worth spending the $14 for your peace of mind.

Another thing you might consider, since Address in the United States is one of the things you can update after your ESTA has been granted, is to update the address (for example with your hotel's address) to reflect that you no longer plan to be in transit.

Some related questions and answers here:

• ESTA, claimed to be in transit but actually visiting
• ESTA Transiting first, then entering the US
• If I have an ESTA approved for transit, can I visit a second time as a tourist?

I asked CBP about this, and their response was…

Question

I applied to ESTA with "transiting to another country". If I wish to stay in US (not transiting), do I need to apply to new ESTA?

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Answer

Once you answer yes to the in-transit question you will not have an option to change your answer. Even though you chose in-transit, the ESTA application will remain valid for travel. We recommend having the U.S. address available to provide to the CBP Officer during inspection.