TurboTax NY State Return won't let me check "direct deposit" for my refund - it's automatically checked "mail me check?"

Yes, you can change your Refund Method.

If you're using TurboTax Online, close the program, clear your Cache and Cookies, re-open TurboTax and go back through the FILE section.

Here's more details on How to Change Refund Method. 

Thank you - I finally figured out how to do this - basically, I went into the New York Tax Worksheet (which I didn't even know about) and was able to change the default there.  Very non-"intuitive" I have to say, but (other than the fact that my refund is less than I'd like) all's well that ends well.  Thank you again for responding though!