There was no Google Street View between 1870 and 1970 -- nor was there a Google, nor was there any internet -- but the OldNYC project is what such a fictional system might look like for one of the US's most historic cities. The project consists of a map of New York City with dots that represent images from that location, and it includes Manhattan, Brooklyn, Queens, the Bronx, Staten Island and even small parts of Yonkers.
Though Google Street View's imaging vehicles weren't driving around in early 20th century NYC, the advent of photography still meant that people were taking pictures. Thankfully, the New York Public Library has saved thousands of these historical photos. The OldNYC project digitizes the images and places them on the map with their estimated date taken, creating a time traveling street view for urban history buffs.