Edit:

There's more than one 'Long Canyon'. I know of four (in southern Utah) that're so-named, but I wouldn't be surprised to learn there were others as well. (Regardless, the number of canyons that're officially named 'Long' falls far behind the number of canyons that're officially named 'Cottonwood'. There's dozens of those, and sometimes it can get confusing, especially when you're talking with someone and they say that such-and-such is in Cottonwood Canyon and you hafta ask, 'ok, but which 'Cottonwood Canyon' are you talking about?)

Been through Hurricane (UT) a number of times but I can't recall having ever stopped at a little diner there, or for that matter having ever eaten a (Philly-style?) cheese steak on Navajo flat bread pretty much anywhere. Sounds tasty though.... Anyhow, there's two primary turn offs for the Burr Trail, and neither are within a hundred miles of Hurricane. You might be remembering the turn-off out of the little town of Boulder, and there IS a really great restaurant within eyeshot of where you'd turn. Haven't eaten there in a while, so I can't say whether or not they've got Navajo Cheese Steaks on the menu. On the other hand, not all that far away from the other turn-off-- the one that takes you down the Notom Road and ultimately to the Burr Trail-- is the resplendent 'Luna Mesa Cafe' (over in the two-horse/three-non-running Chevy pickup trucks up on blocks) "town" of Caineville, and I'd bet a dollar they serve Cheeze Stakes on Diné Flat Bread whenever they're open for business. Which isn't often. Because the owner likes to go out and play at the oddest times (which typically includes times around 'lunch time' when, as luck usually has it, is when I'm typically passing by).

But yup, that other 'Long Canyon' can be kinda pretty, too. This one --the one in the pic-- is more in my area, outside Moab, sorta near-ish to Dead Horse Point State Park.

Oh. And thanks.