I’ve completed 4 ‘round the worlds’. In the 172, there will be places you can’t go due to limited range (Hawaii, Azores, others) but you can circle the planet otherwise. I’d suggeste giving yourself some wiggle room… change aircraft every continent to help with boredom. Flying over North Africa at 100 kts will seem like forever.
Another tip… at every place you stop, Google it and get an idea of what you’d be seeing if it was real life.
Challenge tip… only land at official points of entry when arriving in a new country. (No flying into Russia and landing at a dirt strip.)