Definitely before the Empire state building was built, which began construction in 1930 (Please see: http://www.esbnyc.com/tourism/tourism_history_timeline.cfm?CFID=7742199&CFTOKEN=14771568), but after the Flatiron building was built around 1890. I've been doing Google Searches on some of the photogs., God bless Google and one of the artists, Mr. Irving underhill lived from 1872 to 1960 but seemed to be most active at his craft between 1890 and 1942. One or two of these were by the HH Tammen Co. and they were active around 1905. So in conclusion I'm guessing that these pics are from around 1905 to 1910, especially going by the automobiles in the Times Square card. Glad you liked the cards.
Well before you said anything I was thinking Titanic era--around 1912--just a guess from a lay person because of the look to them.