I'm thinking of randomly taking days off from work just to wander the city
What is motivating you to want to wander around the city?
It helps me reflect on my life.
Taking time off from work is sometimes very therapeutic. If you want to take a break and reflect on your life for a little while, you are more than free to do so. Taking time for your mental health is very important as well.
OMG. I'm fired.
That is very bad news. If you gave your boss notice before taking off than there is no reason why they should have fired you. This sounds like a pretty unfair situation.