The brain devotes more tissue within the for body areas that are highly sensitive to touch such as the lips.

The answer to this question would be somatosensory cortex.
The amount of area that was brain dedicated for an organ is not same as their size. Hands area is bigger than feet. That was because of hand much more sensitive than feet. More sensitive means that there are more nervous per inch area. The nerve distribution density will affects the brain area more than the total surface area.