I could see myself building a habit of wandering around unknown parts of the city.
I can't do that. The 'unknown' parts of my city are unknown for a reason...
For instance, when I lived near LA I would regularly bike all over, including through areas such as Compton.
Seriously.
Can't you just sit there at work, drink your tea, enjoy the view outside the window, the birds, concrete, clouds and noise. Listen how people speak, phones ring, listen to this music, composition of life.
Problem? Turn around and walk away. If problem is not solved by then, then try different strategy. Experiment. Failures are essential to success.
More of life will not help you get away from life.
Also, I did not considered one important factor, you enjoy stress and have opinion that it is must be rid off. >:D