If you are sure it is a town in the Russian Empire, Yanishik is likely Yanishok, the Yiddish name for the town now known as Joniskis, in the Siauliai district of northern Lithuania. Other names you can find on old records for the town are Yanisky or Janizky.
You can look for records on Jewishgen, to see if you find your family there (look in Lithuania, in the Siauliai uyezd of Kovna gubernia). Also, US records like ship passenger lists and naturalization records would likely have the town of origin.
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Rabinowitz in Papile, Lithuania and Riga, Latvia
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus