I'm missing how or why the 8th Ave El (if you mean elevated train) plays into your scenario. Can you explain why the 8th Ave EL was more important than parts of the transportation system?
Rivington Street (runs East-West) is on the lower east side of Manhattan, 8th Ave runs north-south on the west side, they're no where near one another. According to an 1897 real estate map there was an existing building @ 6 Rivington.
Are you using period maps to plot this data out? The address 98 6th Avenue exists in a different place today than it did in 1893.
An affordable and vast transit system made and continues to make NYC extremely accessible. She had the ability to move around the city quite easily and cheaply. The gay 90's, foot loose and fancy free. The locations aren't as relevant in this case.
You mention she married in 1903 and have a bap record for a child in 1915 at St Pat's. Do you know if it was the Old or New St Patrick's? What about other children? Have you tracked the baps of older children? This could give you more insight to the area where you might find the (church) marriage record. These records have the godparents recorded and can lend if there is extended family to put together.
Is the "time stamp" on the photo engraved? If so, where exactly?