Blaine would be an option but it's not like Mewtwo had a phone number or something.
And would telepathy trough a phone even work? Besides.. did Mewtwo know about Vermilion City as Kantos most important port?
How could he came back to Kanto? Even if he knows about vermillion.. he needs a lot of money for a ship to another continent.
That means he need to battle a lot trainers to take their prize money. So.. why not battle gym leaders?
And what if Sirds Hideout is near Opelucid or something? And Mewtwo doesn't even know where Castelia is. And even IF he knows.. he must travel trough the whole region anyway to reach Castelia.
So.. he knows he needs money for a ship. And he knows he must reach a port first. Why not kill two birds with one stone and battle every gym leader on the way. He could find another solution.