{{I am unsure if Greycloaks of Warden Wellington or any PCs dedicated to the Temple of Tyr already have a start/login location at the Temple of Tyr or not.}}
However: Perhaps the Acolyte in the Temple of Tyr could serve as a starting point for those PCs who seek refugee status in New Dunwarren.... those PCs who are possibly in hiding from other factions, or due to the political climate in Sanctuary, or anywhere else. For example, I am thinking of a few Councillors ;) who might need a place to lay low for awhile. I'm sure there are multiple other locations that a PC on-the-run could reset themselves to login at. New Dunwarren just might be a slightly safer option.
Of course, the PC would still have to deal with the citizens (PCs) of New Dunwarren when they encounter them in-game.
I remember briefly seeing a Dirty Nancy NPC on the bedrolls in the Temple of Tyr. My first thought was 'refugee': though I'm sure that all 'lower types' would not be welcome or treated well initially in New Dunwarren.
Such a starting point (offering RP refugee status) might make for some further RP complications between New Dunwarren and Upper and Lower.
Perhaps the simple brown cleric's robes, that all New Dunwarren citizens wear, might become available at the merchants there to.
What do you think?