I have a input text in the form for date and i use JQuery datepicker to select date.
$( "#currentDate" ).datepicker("setDate", new Date(""));
works for me, read at least 10 very complicated ways of doing it and then realised this works. You are instantiating a new value each time. you store the date somewhere in your php scripts, using form input or some other technique and then recycle it back into the above statement. So reloading doesn't affect the result.
If myCurrentDate is unset it will set it by default. Getting it to be set to today's date requires a php if statement to set it the first time (or reload the page) to new Date() and the else statement can be used to include the above code.