Why are villi present in the intestine and not in the stomach?
Because the stomach doesn't absorb nutrients.
Villi of the small intestine are small finger-like projections on the surface. One villus contains many cells and thereby increase the surface area (see image below). This is required because a lot of nutrients have to be absorbed in the small intestine. Lots of cells on a small area makes this process efficient.
The stomach collects the food, adds gastric acid and enzymes for digestion of food. The stomach does not absorb any nutrients and therefore does not require a larger surface area.
There is only a singe layer of cells on a villus, this allows for quick transport to the lacteal vessels (fats) and blood vessels (all other nutrients).