I was just wondering if there is a single word for the person who has recently moved to the new city or new in town.
I think what you're looking for is Newcomer.
(noun) 1. a person or thing that has recently arrived; new arrival:
She is a newcomer to our city.
The firm is a newcomer in the field of advertising.
Newcomer was my first thought but, depending on the context, incomer may also be suitable.
incomer Noun British
A person who has come to live in an area in which they have not grown up, especially in a close-knit rural community.
I've heard people out west say, greenhorn, though typically it means something equivalent to a rookie, it can also mean a newcomer usually to a rural area.
1 : an inexperienced or naive person
2 : a newcomer (as to a country) unacquainted with local manners and customs
This isn't nearly as common as the other answers in this thread, but it's a colorful, American phrase and deserves mention.
1: a late or recent arrival: newcomer