To unlock the CTo unlock the Casino you must rescue the following sprites:
Roller - On 8 Spring, walk towards Vesta's farm, crossing the bridge who runs the Medal Exchange.
And any one of the following:
Press A in front of the well next to the Blue Bar for Hops who runs the Poker Table.
Press A in front of the stove to the left of the Inner Inn for Tep, who runs the Blackjack Table.
Press A in front of the fountain in Romana's Courtyard for Jum, who runs the Memory Game Table.
If you find all three, you can play all three games, but finding just one of the games will open the casino.