Place on Moon that always lit?
This kind of location is called a peak of eternal light.

Apparently there is no certain identification of such a peak on the Moon, but there are definitely places that get more than 86% sunlight during the lunar year (ignoring eclipses). Kaguya did not find any permanent peaks, but there is apeak near Peary at the North Pole that gets 89%, and several places near the South Pole that have multi-month illumination. 

Calculating the requirements for such a peak is complicated since the moon is definitely not spherical on the hundreds of meter scale; at the very least one needs an ellipsoid model. The south pole situation is complicated because there is a large basin around the actual pole.