I think I'd split up Asia, because it's both huge in its geography, but also has regions that are quite different from each other, culturally and even sometimes politically (Middle East v the rest of Asia, for instance). So give a seat each to the Middle East, South Asia, and Far East Asia, at a minimum.
Africa also has a rather firm split in its cultural/geographic composition. It would benefit from a division between Northern Africa and the sub-Saharan nations.
Australia & New Zealand could go with Oceania. That's what all those Pacific Island nations are known as these days.
As for Europe, I think the only way to get the current Security Council on board with a shakeup of permanent membership is to make it feasible for both Russia and, say, France or Germany to have permanent status.
The New World could be divided between North America, South America and the Caribbean. As with Africa, Asia and Europe, the interests are different enough between these three sub-regions to justify the split.
The temporary, rotating members could be one other nation in each of the regional memberships. Or some regions could decide that one of them will serve a 5 year term as their "permanent" council representation, and then do a yearly rotation among the remaining nations for the "temporary" member. Let each region decide which type of representation it prefers.
That sort of reorganization would create a Security Council more reflective of the real world as it's stood for quite a while now.