I believe that a simple and cheap way to discover a new city, including the areas that are out of the tourism circuits or that are not home to a famous or specific attraction it to buy a tickect for a tram and ride it from its origination until the final stop.
I have found so many hidden treasures by roaming around this way and I will keep on doing it.
In my city, Turin, it’s very easy, there are several streecar lines that cross the city for north to south or from est to west. The main highlights are obviously in the city centre but there’s plenty of treasures even in the suburbs that you will not see unless you get the chance to get lost in a different city area.
So jump on my street car, sit close to a window and just admire.