A lot of tourists end up by doing something like this:
They study the maps weeks ahead and in the foreign city they walk with they map constantly through the city and follow strictly the routes that are given.
However, during the last trips my boyfriend and I decided to hide the maps really deep in our bags which are just used in emergencies. We use the maps maybe the first day in order to get a bit of an orientation and then we start to walk on our own. Automatically you don't follow the tourist routes, because you know in which direction you have to go and therefore, you also go into the side alleys. Not only does this strengthens your sense of orientation, but also opens complete new doors in the country.
Personally I recognized that this helps me to get to know the city a bit better. I know this sound super superficial, because as a tourist I will never be able to really get to know a country within 5 days, but it help me at least not feeling like a complete tourist. It helps me seeing other aspects of the world, exploring new things and therefore, feel more personally connected to the city or to any place.
What are your on your trip? Do you also like to walk through a city without a map?
All the best,