Don’t beg for help, it’s a free plugin with free support!
You will need to have basic knowledge of php/js if you want to modify the code to make this work.
I really can’t write out a full step by step guide with code examples, that’s way beyond the scope of the free support. I can make a shorter one though, but you will need to do your own homework a little bit.
– add an input field wrapped in a form tag in the sidebar.php or wherever you want to show the input field.
– Set the form action to the page that contains the store locator page. So if you search for “new york” and then submit the form you should see the city you search for in the url you submitted the form to.
– Grab the searched city from the url with js ( code example on the other page I linked to ), and copy that value to the input field with again triggers a mouse click ( jquery click event is what you are looking for ). This will make the store locator use the value provided from the other search field.
Otherwise you will have to wait until the premium version is ready, which will contain a store search widget.