This question was brought about by the fact that some of my ancestors immigrated from Russia to New York in the 1880's. The source I have for that fact is a citizenship application. Was Ellis Island the only operating immigration inspection station in New York at the time? If not, what other stations were there?
No. During the 1880s, immigrants entering New York Harbor went through the state-controlled facility at Castle Garden.
Between August 1, 1855 and April 18, 1890, Castle Garden was the original immigration station before Ellis Island opened. It handled about 8 million immigrants before the Federal Government took charge of the immigration process. The CastleGarden.org will let you search by name and time period.
While Ellis Island was under construction, the Barge Office at the Battery was used for processing immigrants.
Ellis Island opened in 1892. Between January 1, 1892 and November 1954, over 12 million immigrants entered the US through Ellis Island (timeline). You can search the ships' manifests transcribed from 1892 to 1924.
An earlier facility in New York was called Castle Garden. It processed immigrants from 1855 to 1890. It was replaced by Ellis Island to handle a larger volume of immigrants.
If your ancestor migrated before 1892, you will want these New York Passenger List records from Family Search which predate the transfer from Castle Garden on Manhattan to Ellis Island.
Be aware that this is old-school genealogy that involves scanning the images for a name, not just typing into a search box!