An elderly friend of mine has recently been to Hawaii, staying from the end of May until July 21st, 2014. He has a valid ESTA which expires April 2016. He would like to travel again this coming Christmas/New Year, staying in Las Vegas for Xmas/NY and then travelling onward to Hawaii, where he intends to stay for a further 3 months. Is he able to do this on a current ESTA, or will he need a full VISA?
The short answer to your question is “No, there is no time limit to staying in the US in any one year when entering with an ESTA” but there are a few caveats.
Formally, he would not be staying on the ESTA but under the visa waiver program (VWP). You can therefore find more info about the rules on the official VWP website.
In any case, it's not possible to stay longer than 90 days under the VWP. So if your friend enters in December, spends some time in the US and then travels to Hawaii, he will not be able to stay a full three months there.
What's a little bit more complicated is determining whether he can reenter the US shortly after having spent 90 days there. There is no firm time limit or overall maximum stay during a year, so no rules that would explicitly ban your friend from coming to the US again.
But if he ends up spending more time in the US than in his country of residence, immigration officers suspect that he left the US to skirt the rules and that he is actually illegally residing in the US and deny entry on that ground.
That said, there are six months between his two trips so, I guess it should be OK in this case.