Go onto the Boardwalk, walk up to the ferris wheel and there should be an alleyway next to the bowling alley. In there, the cat spawns in the grass. The cat only spawns at night and only some nights.

The cat sells the following:
Cat Sacks: cat be opened to give a random item (usually worthless) (1,000 units)
Tiny Potion: better than the Small potion at making you tiny!!!! so gr8 (2,500 units)
Cat: Not really. Cat pets are at Toy store.