It wasn’t exactly unexpected for Aegon to leave the castle for his late night visit to the city. More explicitly the Flea Bottom. Your brother the prince was known for sneaking in the taverns, gambling dens in King’s Landing, sometimes even disappearing in brothels of Street of Silk. But not for half a day.
Your mother, Queen Alicent ordered either you or your brother Prince Aemond to find Aegon and bring him back. And, of course, Aemond refused, unless anyone wanted to see Aegon get beaten up in the process. With no choices left you depart for the city.
Night falls on King’s Landing. Streets are bustling with nocturnal activity. Performers singing and dancing here and there, merchants standing by their stalls, commonfolk taking the best of the nightlife of the capital. With no particular idea where to search you move around the streets, dark cloak covering your features - no one should recognize royalty, especially on a mission like this. You are on high alert, your wastrel brother can be anywhere, starting from a tavern and finishing with lying drunken behind the corner in a dark alley.