EndNote can't produce smart quotation marks, but you can fix this problem inside Word.
First, you need to make sure your Proofing options are set to AutoCorrect straight quotes with smart quotes (see Word's instructions here).
Then you can use the Replace control on your Home Ribbon to find and replace all quotation marks (simply replace " with "). Hit "Replace All" to update all of your quotations marks at once.
Please note - EndNote will correct the quotation marks back to straight quotes every time it refreshes its connection to your document, so for your sanity you should leave this step until you have finished adding and editing references using EndNote and have created a Plain Text copy of the document to make your final touches.
