The Neverseen have many Hideouts, many of which were compromised when Tam Song, Dex Dizznee, and Biana Vacker, deciphered the secret of the Lodestar Mirror, the Lodestar map, and how to "teleport" using shadows and locations of the coded map during Book 5: Lodestar. Prentice also assisted by mentally giving them the full map.
The only ones that were named in the books were the Pallidrose Hideout, the Gwynaura Hideout, and the Valkonian Hideout. They were named after stars with pure glows. These hideouts were all part of The Neverseen's Sixteen Former Hideouts grouping.