This page of the Marvel's Spider-Man game guide contains a description of the next mission in the main storyline - "For She's a Jolly Good Fellow". This time, Peter has to forget about his life as a superhero and focus on more mundane matters. It is time to visit Aunt May at her birthday party!
Head to Chinatown and go to the F.E.A.S.T. headquarters - this is an institution which takes care of the homeless. Enter the lobby and you will come across a large number of those in need. You can talk to some of them, although it is not necessary as far as the main storyline is concerned.
Go to the kitchen and take the stairs upwards. There are more objects and characters for you to interact with on the way. Your purpose here is to talk to Martin Li, whom you will find near the dining area. Talk to the man about the upcoming surprise.
A cutscene awaits you now, where the other residents of the institution will surprise Aunt May with a birthday cake. After the scene, you can talk to the others - when you are ready, go to the exit and the mission will come to an end.
You will receive 250 XP for completing the mission. You can also visit F.E.A.S.T. now, and use the facility for fast travel (when you unlock this option later on in the story).