First, there is the Cat's Lair, which is the ThunderCats' base on Third Earth. Read up on that.
Now, onto the places.
Berbil Village- Home of the RoBear Berbils. This is where the Berbils cultivate their Berbil and Candy Fruit.
Castle Plund-arr-Fortress home of the Evil Mutants
Some Mountain-This is where Mumm-Ra summoned Ta-Shi to Third-Earth from her Time-Warp prison.
Black Pyramid-Malignant home of Mumm-Ra on Third Earth. It was hinted that this foul place might have once, a long time ago, been a sanctuary for goodness, not evil.
Snow Castle-The frigid fortress of ice sits atop the pinnacle of Hook Mountain, and serves as the residency for the Snowmen.
Tower of Traps-Baron Carnor made a tower of traps long ago. It held his fabled treasure. Before he died, he created living gargoyles to steal for him so he could just sit back and become rich. He then died, but the gargoyles kept on stealing for a long time and bringing their loot to this tower.
Village of the Wallows-This is where the Wallows live.
