During the day, you'll receive a phone call from Elizabeth, who tells you about a change in Tartarus. Basically, you'll receive a call from her a day or so after a full moon event, where she tells you that the barrier you run into previously will be unlocked. That means you can progress further into Tartarus and it usually means that Elizabeth will have new requests for you, so always make sure to check those out after a full moon.
Anyways, since today is a Sunday, you can access the TV to buy an item from the Tanaka show. Today's items are a Giga Power Band and a Diet Food for 2,980 yen.
Although Elizabeth didn't mention it, there's another thing that needs to be mentioned about today. Visit the Velvet Room and Liz will talk about the Persona Compendium. This is a special book of sorts that will register the Persona you have in it. Any new Persona you obtain will automatically be registered in the Compendium at its base level, and with its base skills. You have the option to register your current Persona(s) in the Compendium, which will update that Persona to its current status. There is a fee (based on the Persona's stats) to withdraw a Persona from the Compendium.