To me both of the phrasal verbs: get around somewhere and go around somewhere mean to go to different places or to go from one place to another in a place i.e. London.
But the only difference that strikes me is that when you get around somewhere it means that you necessarily use a vehicle, but when you use go around it can imply that you either travel on foot or drive to somewhere.
Meanwhile, get around implies travelling which logically requires a vehicle, while go around alludes to just going which can imply travel or just a simple walk.
Do you confirm my take on the nuance between them or there is something else that I have to know?