Poison Ivy's Lair

Poison Ivy's lair is an abandoned hotel in Arkham City. It is located near the GCPD Building. Because Ivy isn't interested in the company of other people, her lair is guarded by henchmen under her control. Catwoman is the only character able to access it as the gate to the hotel is blocked from Poison Ivy's Plants; Catwoman is able to climb under a bridge, circumventing the gate.

Arkham Asylum Incident
When Harley Quinn frees Ivy from her cell, she makes the Botanical Gardens her lair. After The Joker gave her an overdose of Titan, Batman defeated her and she was imprisoned again. She was ultimately blamed for the destruction of Arkham Island by Quincy Sharp and he made sure that she was one of the first inmates imprisoned in Arkham City.

Arkham City Incident
When Catwoman needed help breaking into Hugo Strange's Vault, she headed to Ivy's Lair, and took out her brainwashed armed henchmen. When Catwoman finally got to her, Ivy didn't forgive her for killing some of her plants in the past. After a quick fight, Ivy wrapped Catwoman up in her vines, but was persuaded when she remembered that one of her plants was locked in the same vault. She let Catwoman go and made her plants rip open an entrance to the vault. When Catwoman got to the plant and her loot in the vault after taking out five TYGER Guards, she killed the plant anyway and walked out with her loot.

If Catwoman visited Ivy after the main story was completed, she could see the brainwashed guards worshiping her, and if you talk to her, Catwoman apologized to Ivy and said that it was Strange's fault. Ivy then said that she will kill everyone, and if Catwoman continue to try to speak to her, she will mutter aloud to herself about destroying all of Gotham City.

Arkham Knight Incident
Ivy has no designated lair, but does spend most of her game time in the Botanical Gardens on Miagani Island.

Trivia

 * Poison Ivy's Lair could only be visited by Catwoman due to the fact that the main entrance was smothered by plants, therefore the only way is to Cat Crawl under the bridge to get in.
 * Poison Ivy's Lair used to be a hotel until Ivy took it over with her plants.
 * Poison Ivy's Lair & Penguin's Museum are the only places you could see a TYGER Guard after Protocol 10 (Not including the Challenge Maps).