Neither of those qualify as cities. They are both settlements (now towns) as far as i can tell. Jamestown would need more clarification though as there are quite a few of them.

Most remote city is determined by proximity to the next closest city. There are all sorts of ways of potentially twisting the criteria to get varying results. I have used minimum population of 500.000 as the criteria as it seems to be a standard of what constitutes a city (among other things). On that basis Perth is the most remote at 2104km away from the next closest city (Adelaide) with the added bonus of being on the same land mass.