The Cafe is unlocked at 2-1 and an important part of the game. Here, you can raise affection with your girls by tapping on them or giving them gifts. You can also collect Stamina and Credits that regenerate hourly separate from your main Stamina bar shown at the top of the screen.
How much Stamina and Credits you can generate on a hourly basis depends on the level of the Cafe and your 'Comfyness' level. To increase the level of the Cafe, you must first obtain the item to upgrade the cafe by beating 3-5, 6-5, 9-5, 12-5, and 15-5 for one item per first clear of these stages. Star rating does not matter, all that matters is clearing it for the first time.
After obtaining the item, press the button shown in the bottom right of the image that displays your Comfyness rating. The icon in the provided image says 3000 which is the comfyness level of that particular Cafe so you want to click on this button, then the blue button that will appear in the new window then confirm the cafe upgrade.
Pressing the other button located on the bottom right of the image will take you to the screen with your stored Stamina and Credits and they will be added to your current Stamina and credits shown at the top of the screen. There is a cap to how much Stamina and Credits you can save so make sure to use these before you reach your cap so your cafe can always be generating Stamina and Credits.
To increase the Comfyness rating of a Dorm, you must place furniture in it. Furniture can be obtained from Crafting, Events and other sources.
To raise affection with the girls, simply tap on them. You can tap on them approximately every 4 hours and the girls currently in the cafe are random. The girls currently in your Cafe will swap every 12 hours and you can't gain affection with characters you don't have so make sure to get them first. 1 character can also be called to your cafe every 20 hours using the ticket icon on bottom and selecting the student you wish to call. You can also give them gifts by pressing the giftbox item and giving them the gift to raise their affection level.
They accept all gifts but certain gifts pertain more to their story and character. As a result, those gifts will provide increased bonuses if you can match the gift you are giving them with something they like. The faces above their heads indicate how much they would like the gift you are currently dragging.