Walking is imo one of the big "secret" ways to get to know a city. I fondly recall just getting lost on purpose in major cities, and at the end of the day take a taxi, or bus, or tuk-tuk back to the place I was staying. So many things seen, and tried, and random people encountered from all walks of life, it's one of the best things.
Agreed that walking is the best way to see a city, for sure. I have done similar one day walks across Brooklyn, Manhattan, etc. and always really enjoy the experience. Usually I have a kind of set goal, like “walk entirely across X place.” I think in Istanbul though I mostly just wandered for 100km (over the course of a week.)
This past summer I walked about 124km around Paris over 5-6 days, going in a spiral through all the arrondissements. That was a great way to discover some new neighborhoods.
Another favourite of mine is cycling around a neighbourhood to get to know it; you get a totally different feel for things than from a car - things typically go by slower, and you are somehow just far more able to observe things.