I would say porbably anywhere in the kitchen, especially areas around where you do any frying, especially deep frying.
Also, I’ve found the best stuff to use to remove sticky dust, is oven cleaner. Make sure it’s safe on surfaces you’ll be using it on. Metal, plastic, tile.
Ah, that probably should have been two different posts. The sticky dust is everywhere, not just the kitchen. Any surface, be it horizontal, vertical, angled, smooth, rough, inside, outside, etc. has sticky New Mexico dust. It has been the same everywhere I have lived in this state.
Also, I’m miffed that my mother looks in strange places and evaluates their cleanliness, like the top of my refrigerator. One of the major advantages to having your family ~2000 miles away is you don’t have to clean weird places for them all of the time.