Ship arrivals to Boston are available indexed on micofilm at the Boston Public Library. There is a gap of a few years not indexed, around 1902 if I remember correctly. After finding the ship you want, you call for the microfilm containing that ship's manifest.
To use their resources, you need a library card. The BPL provides them for visitors at a desk just inside the entrance to the new building (left after entering). You need this card to request the microfilms.