When I was a child, grass was the one plant or type of plant that was simplest and most universal. I know that there are places where there are few trees, but are there places where grass is either not found at all, found only as a potted or garden plant with people who have explicitly brought into it in the area and take special care of it, or where it is so rare that finding a patch is something astonishing or special?
As for the definition of “grass”, I would include, at a minimum, all the plants of the Poaceae family, so “grass” includes not only common lawn or field grass that you might find on someone’s front lawn in Pennsylvania, but also wheat, rice, maize, sugarcane, bamboo, and reeds.
As for what size of an area constitutes a discrete land area that can be judged to be notably grassless even though there is grass just outside the boundaries, make a reasonable judgment call. A country where there is no grass within 10 miles inside the border but grass grows within 5 meters on the outside/other side of the border might be notable. An arbitrary 1 square meter section of land in the middle of a highway lane is not a notable area. In a sense, an area that represents a distinct geographical or climactic region can be treated as an area for the purposes of this question. So it’s more like “Is there or is there not grass in the Yukon?” versus “Ooh, there’s no grass under this 5 meter boulder!”
I’m not sure that I would consider the peak of a mountain to be a notably distinct geographical or climactic region, so if there’s grass somewhere on the mountain I would say it doesn’t qualify. After all, there’s often no grass directly on the beach but there is grass within a mile of the shore. The dead zone of Mount Everest might qualify as one can consider that to be a distinct climactic zone.
Australian deserts are arid scrubland, not desolate sandy wastes like the Sahara or the Arabian Desert, and even those sandy wastes have a few plant species that would disqualify them.
(Yes, I know no-one suggested them yet, I’m getting in first.)
In Antarctica grass is limited to the Antarctic Peninsula that extends towards South America. The vast majority of the continent has no grass or other flowering plants.
There are large areas of sand dunes and other bare areas in deserts such as the Sahara, Namib, and Atacama with essentially no vegetation including grass. However, if any higher plants are present in an area at least some of them will be grasses.
In my recent years in the ME, I have seen vast stretches where no grass is visible. Many places that are sand, silt or loess a meter or so away from a dry stream then nothing for kilometers, but if you come back in the one or two day rainy season, the whole area is carpeted in green and flowers.
Perhaps parts of the great deserts would qualify?
In rain forests the amount of shade and poor nutrient quality of the soil generally restrict naturally occuring grasses to along streams and manmade clearings. So they do exist but are relatively infrequent.
The Skeleton Coast in Namibia is probably the most desolate area on Earth. Once you get away from the ocean, there is no fresh water and no life at all.
That was my thinking as well, the same is true for places like Greenland, which is rather mild along the southern coast, but the OP probably only means areas with bare ground for at least part of the year since few, if any, plants are going to grow when covered with snow/ice.
I’m not sure if this fits your definition, but in South Florida grass does not grow naturally. It’s basically a drained swamp. Yards and developed areas which have grass have transplanted sections of sod with grass that has been germinated in it.
Northern Sudan. I spent two weeks there a few years ago and while there is vegetation within about 1/4 mile of the Nile, most of the rest is just sand.
Define “land area”. There are several deserts in Spain where grass is rare to non-existant, but if your minimal size is 100 km[sup]2[/sup] then I think the ones I know don’t qualify. The “small plants” are bushes, crawlers, succulents (think cactii, aloe) or, in arroyos, mosses. They do have their own climates (micro, of course).