Until Optimum Alfred arrives, the Rat Cave will cost 3500 simoleons to build. However once Ava Cadavra has left, Tristan Legend says he needs to see you. There, he will show you to the Rat Cave which is already complete free of charge. This is also balanced out, as players who paid for the Rat Cave see a scenario where Ava leaves her wallet behind containing 3500 simoleons, so either way, you either get refunded for it or get it for free. Once built in either of the two ways, your hotel score will rise by 7%.
The Rat Cave is a unique room in that it unlocks the ratticator, a costume for your sim to wear. This enables them to defeat robots and goons when they're invading. Inside the rat cave is everything your sim requires in terms of needs, except a source of food. Additionally, there's a unique type of chair which can be used to increase sanity.