Welcome to Photrio.
I've tweaked your thread title a bit, because when I saw it I thought of something entirely different than what I believe you intended
By the way, people don't always notice the sub-forum when they read thread titles, so if your question depends on something like a location, it helps to include it in the title.
I hope you get some useful responses.
Go out early in the morning. There are plenty of opportunities in the regular “tourist sites “ for non typical tourist shots. Visit the art museum there are opportunities there as well. The old post office building, the Picasso sculpture and other sculptures in public spaces and the”bean”. I found good material that does not at all look like a tourist shot including an abstract self portrait under the bean with no one else in the image. Some of the hotels have rooftop bars that can give you a bird’s eye perspective.
Through the years I’ve made many effective images at popular locations that are not “tourist shots “.
I do occasionally take a typical scenic shot most are not and cannot necessarily be identified as to the location. I frequently take a phone shot since the gps records the location so I don’t have to take notes.
It really depends on what you consider a "gem." Almost everything everywhere is photographable at some point, it is all in the eye and skill of the photographer and his or her viewer(s).