How do you think the Manderlys managed to flee to the site of White Harbor, which is on the eastern seaboard of the North? As far as I know, the Mander doesn’t link with any river draining into the Narrow Sea, & the Reach borders the Sunset Sea not the Narrow Sea, so wouldn’t it have made more sense for them to flee to somewhere on the Stony Shore or Sea Dragon Point? Plus, why did they flee all the way to the cold North instead of say, the more verdant Riverlands or Vale?

Well, they probably sailed east around Dorne and then up the Narrow Sea.

As to why not the Riverlands or the Vale…the Riverlands is famously fractious and prone to private wars over land, why would any houses stand by and let some king take their land and give it away to a Reacherman when the Reach had been invading the Riverlands since the fall of House Justman? And what Riverlander king would have the authority to make that stick? 

Likewise, the Vale is pretty small and the lands had been divided up early on, which is one of the major reasons why the Andals had invaded the Riverlands with the encouragement of the Arryns – not enough space, need to get people to emigrate. 

Whereas the Starks had vacant land, because the Wolf’s Den was not being properly held and had been repeatedly attacked by the Arryns and the Sistermen and slavers from the Stepstones. The Manderlys offered an opportunity to solve a major security problem without the Starks themselves having to pay for it.