Hehe - I'm off to Texas in two weeks' time. But I'm giving myself leeway, as I used to live there and hence have my favourite restaurants to visit - I haven't been back in 10 years. But I do feel your pain, as without leeway it'd be extraordinarily difficult.
I was just in NY and the temptation there was ridiculous. But yes... hotels do generally have eggs, bacon, okay things on menus for breakfast (and pancakes, and waffles, and amazingly sweet cinammon buns, which oddly enough aren't on standard hotel menus here
).
And it's America - certainly in Texas, you can always ask restaurants to substitute one food for another. The menu is more of a guide than set in stone. Which always flummoxed me and I never dared order anything off menu, and then watched as friends basically customised their plates to their liking! Plus you can generally ask for salad dressing on the side, so they don't douse it all over your salad. US salads are amazing. And big. Have courage - ask the wait staff to help/not put the carbs on the plate!
I went to an amazing breakfast place in NY that was a chain, and it had a whole variety of very low carb breakfasts, except they marketed it as healthy or some other inspiring, hip word. But they had the nutritional info printed too, so it was easy to pick out. I had an amazing spinach, chicken, avocado, mozzarella cheese wrap there, that was wrapped in something that wasn't bread. Sorry - I can't remember the name of the place.
I think it must be US policy now (for chain restaurants at least) to put calories on their menus. That was a disarming sight. I think I'm going to be in for a shock faced with Texas-sized portions again.