Right after Sato left the room, he headed straight towards the nearest NPC store where he purchased a few materials with the proceedings from the sale of the [Balk Rose Armour] following which he then left for the blacksmith guild to improve on his skills.
As for the others, since they weren't blacksmiths like Sato, they went levelling up outside of the city rather than to waste their time inside the city. According to the plan from Sato, once the tournament was over, they would test-run the dungeon to see how far they can go so the team had to make preparations. Sato was level 16 so he didn't need to worry much about his level. But the others averaged around level 10 and 11, which wasn't enough for them to explore the dungeons. In Sato's own words, level 13 would be the basic for them to check out the place.
24 hours later...in real-time...