The exterior of Nepeta's hive was never seen. It was built into a cave, but never shown from the outside. Her blood color places her in the Lower-Middle Class, so the plain architecture of her hive may reflect her status. The building was later expanded by Eridan Ampora to reach the Seven Gates and eventually Skaia as required by Sburb, but was ultimately destroyed alongside Nepeta's whole planet during Jack Noir's rampage.
Nepeta's respiteblock is the inside of a cave. It is eventually partially destroyed by a cave-in, killing her Lusus, Pounce de Leon. She does have a single piece of furniture, a grey table which holds her computer of choice, a drawing pad. She clearly loves to draw and the walls are covered in ash, blood, and soot. These scribbles include the Shipping wall that she uses to ship her group of friends. She and her lusus seem to have killed two beasts that make for squishy throw-rugs. Who doesn't love the feel of dried blood and fur in between their toes in the morning? Part or all of the wall is apparently at the edge of the cave, shown by how Nepeta has multiple windows with a clear view of the sky. This would suggest that her hive, or at least her respiteblock, is built into the side of a mountain.