How did Holmes guess that John Garrideb would go to 136, Little Ryder Street? Did he expect to find what he ultimately did before he went there?

Holmes had known that the whole Garrideb story was false after the first meeting with John Garrideb itself. After visiting Nathan and encountering him there too, he realized that his aim was to get Nathan out of his apartment. He then visited the Scotland Yard where he found out that he was Killer Evans and the link to the apartment was that it was where a criminal, Presbury whom Evans shot, had stayed. So yes, Holmes did expect to find what he did.