Market Square, Providence (circa 1900)

Dating this, the 1-cent Franklin, introduced in February, 1903, was produced in enormous quantities (11.2 billion) largely to support the postcard mania of the time. The stress of this high volume on the Bureau of Engraving and Printing can be seen as the initial color of apple green became a muddy, blurred green by 1905.

So it's a good guess that this is about 24 September {1904}.
The card would have been issues from images dating to 1900 just as Lovecraft was turning ten or so. It shows the church, and many other iconic images of his childhood.