Well, for starters, I'd simply charge breakfast on my SPG Amex and then look online a couple of days later to see how it hits your account. If it hits your account as "Altanta Westin" (or whatever), you're in business. If it hits your account as "Joe's Bagel Shop", you aren't.

Only reason I don't suggest asking the waitress/clerk is because they aren't going to have a clue. But you could try...

Usually, if it's the standard hotel casual-dining eatery where they set up the breakfast buffet and that kind of thing, you're good. In most cases you can tell when it's not going to be a hotel charge - for example, if it's a name-brand restaurant like Ruth's Chris or something.