Looking at the map, you got three major options. One, you can go through the mountains you first arrived in. The centaurs avoid it like the plague, since apparently there are very powerful monsters common there, like the basilisk you killed. One is forested path, that is a bit longer, but won't be completely free of centaurs, while having a major monster presences, though far less strong ones than those of the mountains. And finally, the original path that takes the roads will be highly patrolled by the centaurs, but would be clear of monsters for the most part.
Spoiler (click to show/hide):
Don't have anything uber concrete. Am open to suggestions but basically mountains would be only monsters for the encounter table but few in number yet very strong. Forests will have a mix of centaur patrols and monsters, that are weaker but tend to operate in packs, while the roads would be pretty much just centaurs with maybe bandits thrown in.
Random person in the comments section of a random hentai manga- "Now I am ashamed of myself."
Me- "Posh, shame is for fools and people with friends... we need no such things, we have the internet."