Alongside mandatory tourist sites, we love just doing ordinary stuff while travelling. We've noted before that for us, the 3 day mark (in one place) is an important threshold. It seems that you get past the 'must do' visits, get oriented re public transport and can make time just to hang about.
Yesterday we took a train out of town to a lake. I had a swim, Maria took some photos, and we loved watching numerous groups of locals go about the beach BBQ, Japanese style. Lot's to love about the experience. We spent a couple of hours loitering in a nearby park where Maria ended up sharing a waterside rock with a little girl as they watched a duck paddle around.
...and more often than not we turn the other direction to the tourists when looking for something to eat. Not only does it save stacks of dollars, the food experience is almost always more interesting. (we ate way too much this night!)