I'm assuming that you would be referring to the "peak" of a mountain. The peak of the mountain is generally the tallest point; thus opposite of the base.
the peak of the mountain
the oppposite OS the base of a mountain is the summit
The opposite of the base of a moutain would be it's peak. The very tip of the mountain where all the snow rests and where it's coldest.
an antonym for that would be at the mountains base
An antonym is the opposite term. The opposite of the base of the mountain would be the top. Another term for this would be the peak or the summit. You might also say the climax or the cap.
The fat end that's connected to the land, it's opposite the pointed end.
The opposite landform could be a lowland. Or in the ocean, a trench, deep or abyss. In mountains, the natural opposite of a peak is a valley. The opposite structure of a mountain, where the elevation is lower rather than higher, is a crevasse or chasm.
base of a mountain
The base word of mountaineering is "mountain."
A gorge.
The Peak
mountain