Currently, Bulbapedia is listing the Orange Archipelago and New Island as directly south of the Sevii Islands, which themselves are directly south of Kanto. The reason is this anime map (caution, huge image). However, on this map, the islands are insets, "much like Alaska and Hawaii on a map of the US". Now, if this was the only map, I would be inclined to believe it, but it is not. A clearer map was included in Pokémon Extreme, which shows the islands on the map itself, along with Kanto, and not as insets.

It was argued that the real world equivalent of the Sevii Islands is located approximately there, but it was also stated that the orange Islands have no real world basis. Therefore, the Orange Islands could be anywhere, and we have a map showing us where they are.

To further prove that the current locations are wrong, here is an item of trivia from New Island:
Quote Originally Posted by New Island
In Mewtwo Strikes Back, the distance from the port in Kanto to New Island is shown to be rather short. However, this was before New Island was retconned to be between the Sevii Islands and the Orange Archipelago.
New Island must be as close to Kanto as depicted in the Pokémon Extreme map, not as far away as it would be if we ignore the fact that the anime map uses insets.

Further arguments:
Talk:New Island#Location
Talk:Sevii Islands#Anime Map Needed