To travel under VWP, travel purpose must be permitted on a visitor (B) visa, as mentioned as the first point in the Visa Waiver Program page. This means, your ESTA is basically a simplified B1/B2 visa, same rules apply, the difference is the process only.
Now, checking the rules for both B1 and B2 visas lists nothing about your specific “writing” purpose, but indeed it does allow you to travel for “holidays” purposes, which is the main purpose of your travel as you mentioned.
The only thing that was mentioned a few times with emphasis is “getting paid from a US based entity”, which is totally prohibited for holders of B visas, that means also prohibited for people on ESTA, and you explicitly mentioned that you are not going to make money, so we can safely assume that you will be fine doing your writing in your free time while you are on a “vacation” in the US.
The closest thing I could find in the rules that might be similar to your situation was “researching”, and the rules allow that:
Independent research, no salary/income from a U.S. based source, or benefit to U.S. institution.
Conclusion: There is nothing in the rules explicitly prohibits you from writing while you are on a vacation in the US as long as you are not making money out of it from a US based entity. So, feel free to write.
Credit:stackoverflow.com‘
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