Most first visits stop at the thing on the postcard. In Paris that is the tower. In Rome the arena. In Tokyo the scramble. Fine. Then there is a second place in the same city that is not a sequel: the Louvre after the lawn, the Trevi after the Colosseum, Shibuya after the temple.
The second stop is how you find out whether you like the city or only the landmark. It does not have to be famous. It has to be in walking or one-train distance from the first. If you cannot do two things without an airport, you are not in a city. You are in a transfer.
Leave the third thing. The week is not a museum of itself.