The first save point they'll find is at the playground, after the cutscene where they first meet Mari and Basil and look through Basil's photo album. Once they're done with that, they can go back and interact with the picnic basket, which opens up the save menu.

To achieve the Secret Ending in OMORI, the player must make sure to water Basil’s flowers each day while in Headspace. The watering can is found after the second time the player finds themselves in Headspace; use it on wilting flowers to water them. This will also allow players to gain the ‘Green Thumb’ achievement.

Starting from BASIL's house (again, you should have a backup save at this point), go back to sleep. Upon waking up again, go to BASIL's room and talk to everyone. Go home, then go to sleep in your bed. Upon entering WHITE SPACE, leave it the way you know how to. Go out your front door and into your mom's car.