If you are on a Beach and looking out at the Ocean, and your eyeballs are 2 meters above the ocean, the horizon is 5 km away:
http://www.tjwalking-madeira.com/horizon.htm
If instead you were on a 1000 meter tower at the beach, the horizon would be 112.9 km away. At the equator every 15 degree of longitude equals is a one hour time difference in a day. One degree equals 4 mins, and one degree is about 111 km. So on top of the tower you would get 4 mins more of morning light, and 4 min more before dusk- giving a total of 8 minutes of more daylight. If instead you were on a 9000 meter tall mountain, your horizon would be 338.6 km, giving you 24 mins of extra daylight.

On the Moon you can see about half the distance to the horizon than compare to on Earth. Unfortuately there isn't a calculator for this so you can use the formula on this page:
http://www-istp.gsfc.nasa.gov/stargaze/Shorizon.htm
So from 2 meters high the horizon is 2.64 km away. And from 1000 meters high the horizon is 58.96 km away.
Now if you take the circumference of Earth, it's around 40,000 km and you divide this by 360 degrees, you get about 111 km per degree. On the Moon it's circumference is about 10920 km and if you divide this by 360 degrees you get 30.3 km per degree. So from 1 km high tower you can almost see two degree of longitude if at the Moon equator, you would need 1060 meter high to see 2 degrees.

On Earth at 4000 meter high you see 225.7 km to horizon- a bit more than 2 degrees and you get about 16 minutes of added daylight. On the Moon each lunar day/nite is 28 days long, so a 1060 meter tall tower at the equator would add 7 hrs and 28 minutes of daylight per lunar day [16 minutes times 28].
The Moon has 1.5 degree tilt in it's axis, it's arctic circle is at 88.5 degree latitude. And the distance from the arctic circle to the lunar pole is 45.5 km. If the Moon didn't have a axis tilt, and there wasn't any hills or mountain at the pole, you could see the sun continuously from the pole. If you moved away from the pole by 2 degrees and had a tower which was 1060 meter tall, you would have continous sunlight. With a 1.5 degree axis tilt you can only be .5 degrees from the pole with your 1060 meter high tower. The Moon, of course, has mountains- mountains and basins as high and deep as on Earth. If there is modest size mountains within 15 km of the lunar pole and if you picked the highest one, than it might have continous light at it's peak- assuming that another mountain isn't blocking the sunlight.

Anyhow, there's a story:
"Scientists have discovered a mountain on the moon where the sun never sets, which might become the site of a U.S. moonbase.
The "peak of eternal light," as it is called, is on the rim of Peary, a 50-mile-wide crater at the lunar north pole.

The peak, announced by scientists from Johns Hopkins University at a meeting of astronomers in Houston, was discovered by analyzing images take of the moon's poles by the Clementine spacecraft in 1994."

http://www.spacedaily.com/news/lunar-04l.html