Sun-Earth
The L1 position is useful for solar observations since it is near the Earth but in constant sunlight. It could also be useful for collecting solar power. Conversely, the L2 point is perpetually in the shadow of the Earth, and as such offers a prime location for observing the outer planets or deep space. L4 and L5 colonies could be used as waypoints in space travel, to expand the practical launch window for travel to and from the Earth and other planets. These positions are useful for colonies as they are stable without any need for stationkeeping.
Read more about this topic: Lagrange Point Colonization