When I land in a new city, I spend the first day with no plan, just wandering about. It's surprising how much of a feel you can get for the texture of daily life in a city by doing this.
From my perspective, food and all the rituals and customs around it are some of the richest parts of culture, so I also like to go to grocery stores like this article covers. Another half-day is dedicated to a food tour, which is a fantastic way to learn about a new culture. In my experience, often the tour guides have lived in that culture for many years but they're not originally from there, so they can do cross-cultural translation for you, pointing out things you might not expect. And the best tours also include walking around the city and seeing cultural highlights.
From my perspective, food and all the rituals and customs around it are some of the richest parts of culture, so I also like to go to grocery stores like this article covers. Another half-day is dedicated to a food tour, which is a fantastic way to learn about a new culture. In my experience, often the tour guides have lived in that culture for many years but they're not originally from there, so they can do cross-cultural translation for you, pointing out things you might not expect. And the best tours also include walking around the city and seeing cultural highlights.