Going to local parks is a favorite activity of mine.
If you really want to get to know a place go to the park, better yet pick up a snack or picnic meal at the local market and make a morning or afternoon of it. You can tell a lot about a place by its parks and how they are used. When I have time in a city I like to walk through parks and people watch.
A lot of times there are sculptures and other decorations that are fun to see. Or just a good view.