Why did Silas go to the Rainbow Inn?

Silas went to the Rainbow because it was the most logical place to inform the authorities (those in charge) that he'd been robbed.

The robber must be laid hold of. Marner's ideas of legal authority were confused, but he felt that he must go and proclaim his loss; and the great people in the village—the clergyman, the constable, and Squire Cass—would make Jem Rodney, or somebody else, deliver up the stolen money. He rushed out in the rain, under the stimulus of this hope, forgetting to cover his head, not caring to fasten his door; for he felt as if he had nothing left to lose. He ran swiftly, till want of breath compelled him to slacken his pace as he was entering the village at the turning close to the Rainbow.