My grandfather was born in Vourlia, Lakonia, Greece and arrived by ship to America somewhere between 1890-1940.
His name was Karabineris Nikolaos (Nick), son of George.
How can I find his immigration record?
Did he become a US Citizen? Or at least start the process? (You might be able to discern this from looking at census records, voter registration records, and/or military records.) If so, look for his naturalization records first, and work backwards from there, since they will have the information about what ship he traveled on, and to which port, and under what name, and on what date.
Get USCIS to do a $20 search for you, here: https://genealogy.uscis.dhs.gov/ They'll probably take a few months to get back to you. If they find a file number for you, you can then order it from them for another $20 and that will take another few months. Those fees are going to be greatly increased soon, so I would order right away.