I think I heard rumors that they're thinking of having Hobgoblin in the next film.
To answer you, the problem is that I have to reveal some key elements of the story, actually most of the plot! (^_^')
It would be a shame if somebody reads my answer without watching the film first...
So, I strongly advise against reading my answer below before watching the movie.
You will ruin your own enjoyment!
I don't think that a new Goblin will be the next villain. It is possible but I don't believe it.
First, the Green Goblin killed May. It is impossible to overmatch this.
Then, the 3 Spider-Men cured Norman Osborn of his mental illness thanks to a serum that Spider-Man 3.0 & Norman Osborn had elaborated.
Also, Ned Leeds learned from Spider-Men 1.0 & 2.0 that their best friend, Harry Osborn, had tried to kill them. So, Ned promised Spider-Man 3.0 that he would never do the same.
During the movie, Norman Osborn was totally lost in the MCU because there is no Oscorp in this world contrary to the other 2 realities.
At the end of the movie, Doctor Strange corrected what happened to the MCU and Spider-Men 1.0 & 2.0 and their respective villains were sent back to their own realities.
Most people in the MCU may have fragmented memories of the events because their remembrance of Peter Parker was erased in the process.
The most significant villain that one of the Spider-Men has yet to meet is Kraven the Hunter. My bet is still on him.
So did Andrew Garfield Spider-Man and Toby Maguire Spider-Man forget who Peter Parker was also? That's how everyone got sent home right. I guess they went home with a sever case of amnesia.
And what was up with the Statue of Liberty? When we first saw it, it was holding up a shield and was covered in scaffolding. Then at the end it looked like our normal statue. I know a lot of scaffolding and the shield got ruined in the fight but it didn't look damaged and it was holding up the torch. Was it an alternate universe statue that knew Spider-Man's secret identity?