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.