After you visit another Your Sanctuary, Dr. Andonuts repairs the Sky Runner and you go to Summers.
Explore Summers
The shops in Summers are overpriced. Buy Lucky Coins, but don't buy the other goods. You can get them for lower prices elsewhere.
The only free telephone in Summers is in the Museum.
Get Photos Taken
Go toward the stairs of the Summers hotel to make the Photo Man take your picture. Then go into the Summers restaurant and walk between the upper left tables to make the Photo Man take your picture. Then walk onto the Summers beach and find a beach umbrella near a sombrero-wearing vendor who is selling gelato. Walk to the right of that umbrella to make the Photo Man take your picture.
Meet the Magic Cake Lady
Go into a nearby house and talk to the guy there to learn the phone number of Club Stoic.
When you go outside, Jeff's friend Tony calls you. He asks for the player's name. You can enter your full name, or your first name, or some fake name, or a nickname, or some famous person's name, or whatever you prefer.
Afterward, go use the museum's free phone to call Club Stoic and make a reservation.
Go into the club, and talk to the man who is sitting at the table on the left. He points out the Magic Cake lady, who is standing by the door. Talk to the Magic Cake lady. If you talked to the guy sitting at the table, the Magic Cake lady will realize that you want her to make Magic Cake for you. Say Yes when she asks if you want Magic Cake. She will leave the club.
Eat some Magic Cake
Go outside and find the Magic Cake lady's cart, west of Club Stoic, south of the shop and restaurant. Talk to her and she makes a special Magic Cake for you.