Episode 2 opens with a time-skip seven years into the future, when Dio and JoJo have made up and become friends and are winning sports games together with their massively overmuscled bodies.

I wanna say they’re playing rugby, but I’m not a sports games expert. I’m an anime expert.
Then, Dio gloats inwardly and says “Aha! But I have only been pretending to be his friend for these past seven years in furtherance of my goals!” And then, JoJo starts wondering “What if Dio has only been pretending to be my friend for these past seven years in furtherance of his goals?” And they’re back at each other’s throats, making the whole timeskip seem sort of pointless. The only thing that seems to be different now is that they both have more muscles. I’m not saying I wanted to watch seven years of nothing happening (although I do consider myself a Hidamari Sketch fan), I’m just not sure why they felt a need to write “and then for seven years nothing happened” into the plot.
So anyway, JoJo suspects Dio of poisoning his father. And you can take that sentence on either interpretation – he suspects Dio of poisoning his biological father to death, and being in the process of poisoning his adoptive father as well. So he takes the suspicious medicine Dio has been feeding his father and goes on a quest to get it analyzed chemically to prove his suspicions. Somehow this leads him to a bad part of town, where he is assaulted by ruffians. He takes their knife wounds in stride and responds with an appropriately modulated amount of force to disable but not seriously harm them, because he is a true gentleman and not a poor like them.

Not everybody has siblings. It’s a shame, they’re great.
JoJo’s forbearance impresses the leader of the ruffians, a man named Speedwagon. That’s literally what his name is. I could forgive the name Dio Brando, but Speedwagon is a bit beyond the pale, don’t you think? Anyway he tells the men to stop stabbing JoJo and offers to help him on his quest.
Meanwhile, Dio is getting drunk and playing around with an ancient stone voodoo mask. It turns out that the mask turns people into vampires, which Dio discovers when he turns someone into a vampire. The vampire almost eats him, but it’s destroyed by a conveniently-timed sunrise. If all of this description seems a little disjointed to you, it seems a little disjointed to me too. There are too many plot threads in the air at once that don’t seem to bear much relation to each other. I have no idea what the hell is going on with the stone mask. It just turns people into vampires for no reason. Why not. This show is flashy, but I sure hope it gets some coherence in a hurry. I sort of suspect that maybe this is all backstory, and that it seems disjointed because they’re rushing through it, because there’s a lot of backstory and they want to get to the real fun stuff involving Archeology and Vampire Hunting and whatnot but they have to wade through all this tedious “who poisoned whose dad” bullshit so that we know why the hero and villain hate each other later. Although man! They hated each other at the end of last episode! This episode was totally unnecessary.