I visit new cities quite often. In order to enjoy the visit without just hopping from one tourist attraction to another I always look for alternative ways to see the city. Anything that helps to get out of the tourist mainstream and enables you to get a different perspective is more than welcome.
So what are creative ways to explore a city. Really anything goes.
A few ideas I like to apply are:
grabbing a map, look for the street index. pick two random streets, draw a line between them and try to follow this like as closely as possible
going zig zag: leave the house. turn left at the first corner, right at the second and so on. Stop when you're tired :-)
my favourite: The barkeepers drive. Go to the first bar/cafe/bistro in your sight. Have a drink. Afterwards ask the barkeeper for his favourite bar. Look it up, go there. Rinse and repeat till you forget where you are :-)