I imagine that the Rangers used the ruins of Fornost rather like Weathertop, or even as the High Elves used Wood Hall ..not maybe as a permanently occupied base but as a meeting place, where they could leave messages and maybe basic supplies (remember the stock of kindling at Amon Sul). Even for a people as resourceful as the Dunedain, this kind of thing is useful - and as has been pointed out it is handy for the Shire - rather closer than the Havens which is the nearest permanent settlement where the Rangers would have been actually welcome. And of course as a trade route used by dwarves as well the route to the havens would be much less discreet.
The place's reputation for "hauntedness" would have been a bonus for them to prevent outsiders meddling in what was a long term covert operation of protecting the Shire.
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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