This is by no means an exhaustive list of locations, and players are not limited to exploring only what's listed here. Again, the universe is a big place. Planets from non-DC universes are also present, such as Cybertron or Tatooine. Players are also encouraged to just make up planets wholesale to fit their needs, and those planets will also be added to the list.
Planets Native to the DCU
Description: ??? is the headquarters of the Orange Conglomerate. It is a fully urbanized planet, featuring numerous skyscrapers and countless lucrative businesses of varying legality.
Description: ??? is the headquarters of the Indigo Tribe.
Description: The Daxamites are an offshoot of the Kryptonian race. Though the star Daxam orbits is red, a Daxamite under the light of a yellow sun gains great powers. Daxamites are not vulnerable to Kryptonite, but instead, are vulnerable to lead. Daxamites are incredibly xenophobic and rarely leave Daxam, despite being technologically advanced enough to make it feasible.
Description: Corps members are... generally discouraged from visiting Earth. It is absolutely rife with superheroes, making it capable of handling itself and/or a bad place for anyone not so morally inclined to be. It's not strictly off limits, but anyone who spends too much time there may find themselves with a "friendly" visit from one of the two local Green Lanterns.
Description: Htrae is better known as Bizarro World. It is cube-shaped and opposite Earth in all respects, to the point of ridiculousness, in case that wasn't already made apparent by the cube-shaped planet. Corps members are generally discouraged from visiting Htrae for their own sanity.
Description: Corps members are discouraged from visiting Korugar. This is Sinestro's home planet, and when he was a Green Lantern, he ruled it with an iron fist. The people of Korugar have thus come to associate the symbol of the Green Lantern Corps (and the other Corps by association) with this terrible regime and any Corpsmen discovered on the planet will be chased off with as much force as can be mustered.
Description: Mogo the Living Planet is a very important member of the Green Lantern Corps. One of the many key services he provides is acting as a psychiatrist of sorts to the GLC. Stressed GL's are always free to take a brief vacation to Mogo, taking in his lovely scenery and talking to him about their problems. He is instantly recognizable from space by the vast band of forest around his middle with a clearing in the shape of the Green Lantern symbol in its center.
Description: Oa is the headquarters of the Green Lantern Corps. It is heavily fortified and completely urbanized, as many Lanterns spend a lot of time there. (It's the permanent residence for a number of them, even.) Honor Guard Lanterns Guy Gardner and Kyle Rayner run a bar called Warrior's there featuring Earth cuisine and it is a frequent watering hole for many Corpsmen.
Planet: The Obsidian Deeps
Description: The Obsidian Deeps hold an unspecified number of planets, but are noted for the complete lack of light. At least one of the planets in the Deeps is home to a race of blind, silicon-based froglike creatures.
Description: Odym is the headquarters of the Blue Lantern Corps. It is a beautiful, peaceful planet, full of flora and fauna. Calling it a paradise wouldn't be much of a stretch.
Description: Qward is the headquarters of the Sinestro Corps. It is located in the anti-matter universe, "below" the regular universe.
Description: Rann is an advanced, urbanized planet. It has recently been involved in a long, brutal war with Thanagar.
Description: There are two species of Thanagarian: the tribal lizard-like people of the surface, and the urbanized humanoids on cities built above it. The humanoid Thanagarians oppress the lizard-like ones. The police force of the humanoids is distinguished by their use of attachable wings. Some versions of Hawkman and Hawkwoman from Earth's Justice League are Thanagarian police. Thanagar has recently been involved in a long, brutal war with Rann.
Description: Ysmault is the headquarters of the Red Lantern Corps. It features a large number of very active volcanoes.
Description: Zamaron is headquarters of the Star Sapphires. The planet features a great deal of violet crystal.
Planets From Other Canons
Description: Aiur is a lush, jungle planet, populated by the technologically advanced and psionic Protoss race.
Planet: Betelgeuse Five
Description: Betelgeuse Five is a small, seemingly innocuous planet orbiting the red giant star Betelgeuse. Not much is known about it among the Corps, as anyone who ventures to explores it reports something about a Pan-Galactic Gargleblaster and then is never heard from again.
Description: Cybertron is a fully mechanical planet, home to beings known as Transformers, which, as the name may suggest, are capable of transforming themselves into alternate modes, traditionally vehicles of other planets. They are engaged in a brutal civil war, divided into Autobots and Decepticons. This war appears to have been going on for millennia and shows no signs of stopping anytime soon.
Description: Namek is home to a race of green-skinned humanoids thought to have evolved from plant life. While Namekian culture seems to be fairly technologically advanced, it is small and scattered, and most of the planet is barren uninhabited wilderness. The Namekians possess a treasure they call "Dragon Balls" and legend has it that if all seven are brought together, a dragon that will grant any three wishes will appear.
Description: SR388 is a rocky, inhospitable world, home to strange, jellyfish-like parasites known as Metroids.
Description: Tattoine is a desert planet that orbits dual suns, harsh and unforgiving. It is home to a wide variety of species, ranging from human-like to insectoid to sluglike and most everywhere in between. Notable features include the popular sport of pod racing, a thriving black market, and the existence of open slave trading.
Description: Thundera is a generally Earth-like planet, home to a technologically advanced race of feline-like humanoids.