The geography of the world as you know it is almost exactly the same as it is in the real world. Seven continents, five oceans. Simple enough. However, the machinations of fighters have somewhat changed how people look at the world and cities that reside in it.
The first thing is, the world's major metropolises are far more international than one would normally expect. "New York City" and "Tokyo" do not actually exist in the world as you know it, and have never actually existed. Rough analogues to the above are, respectively, the world's "Metro City" and "Southtown." Both of these are to varying degrees American hybrid cities, harboring large subpopulations of most nationalities within and with very few language barriers for newcomers to breach inbetween.
The largest subpopulations of fighters tend to hold residency in one of the two major cities. The concentrations of fighters in either city means that the public of those cities are somewhat inured to seeing fighters and fights out and about in the streets, and so fighters can live something kin to a normal life in either. This is not the case in places such as the village in India where Dhalsim lives, where he is regarded as a major celebrity and risks attracting onlookers wherever he goes.
In addition, the actions of fighters can change the scope and impact of the world's geography, sometimes even at will. At one end, areas that were once mere footnotes of history to the common man have become hypersensationalized in the public eye for being the site of major martial arts battles. The Lying Buddha statue from the Ayutthaya Ruins in Thailand is well known as being a site of reverence for those who practice Muay Thai. On the other end of the spectrum, cities can bear the scars from major fights for years, and many home, commercial and auto insurance companies have specialized claims adjusters and plans for collateral damage from fighting, oftentimes subsized regionally through taxation of the many tournaments that draw crowds there.
Beyond even that, entire landmasses have been ravaged, or have even disappeared underneath the might and strength of fighting terrorists, factions, and even certain unknown godlike individuals. These acts have been variously been looked at as awe-inspiring, religious, or even crisises on the order of natural disasters. Many have often been criticized and condemned by many organizations and world leaders as the result of fighting excess, and governments are often judged by their citizens by their ability to repair, minimize or protect the populace from such damages.