LECTURE today, so choose to stay away to increase Academics or doze off for a chance to increase your condition.
After school is over, you're shown a little note that mentions that you'll be able to spend your afternoons in any way you want. There isn't anything you can really do now, so go downstairs and exit the school to view a small cutscene. Exit the school's grounds to be taken to the town map, then select Paulownia Mall (for details about the other options, check the Game Basics section).
At Paulownia Mall, head straight to the police station and head inside. Akihiko will introduce you to Officer Kurosawa, who will be your main shop for weapons and armors. Akihiko will give you 5,000 yen, so feel free to buy any equipment if you want. The police station is only open to sell equipment during the day and he gives a discount on Mondays, so if you do any shopping, do it on Mondays.
Once you leave the station, Junpei leaves and you're free to do anything you want. Since you don't have any Social Links to work on yet, feel free to work on one of your attributes. You can also visit the other shops (pharmacy and accessories shop). Once you're done and the time has progressed to the evening, you'll be back at the dorm.
Once you're back at the dorm, Mitsuru will mention a few things about being able to explore Tartarus anytime you want. You can only explore Tartarus, for now, if Mitsuru is at the dorm and sometimes not all of your party members will be able to go (they have other plans). You're also able to freely go out at night, but for now the only things you can do are work on your attributes mostly. If you don't do anything during the night and go back to your room, you'll have the option to either study (increases Academics) or sleep earlier (improves condition). Do whatever you want.
Note that if a day isn't listed from now on, it means there isn't an important event that happens and it's a free day for you, so you can work on Social Links, among other things.
