Does anyone know of any movies about starting over or moving on...and/or perhaps about someone moving somewhere completely different and foreign to them, like from a small town to a huge one like NYC?

Thanks ahead of time.

Well I saw two movies in the last few days and both can fit your description:

Closer (a little loose but it can fit)
Scarface

I'll think of more.

In America
Coming to America
Joe's Apartment
Barton Fink
Ghost House
Rumble in the Bronx
An Autumn's Tale
My Blue Heaven
Mosquito Coast
The Experts
Get Shorty
Secret of My Success
Orgazmo
Hudsucker Proxy
Beetlejuice
Casper
Jaberwocky

Funny Farm, where Chevy Chase plays a big city sports reporter who moves to a Norman Rockwelleaque town.

I also remember some movie series from the early 80's, called something like The Wilderness Family. The family's daughter has bad asthma so the family moves out into the woods.

Three Colors: Blue
Lilja 4-ever
Diary of a Country Priest
Nostalghia
Red Beard
Lost in Translation
Stranger than Paradise
Morvern Callar
Y Tu Mama Tambien
Uzak

28 Days Later-- moving on after the catastrophe
AI-- starting over/moving on after the abandonment
Annie Hall-- moving on in relationships
Appleseed-- main character starts over in the big city
Barton Fink-- Barton starts over as a movie writer
Being John Malkovich-- several examples of starting over AND moving on
Blue Velvet- main character comes back to his hometown
A Bug's Life-- the circus bugs start over
Close Encounters-- main character changes his entire life to center on his new obsession (the aliens)
Darkman- moving on from the trajedy in his lab
Drugstore Cowboy
Fisher King-- Jeff Bridges character starting over, Robin Williams character moving on
Iron Giant- starting over on earth without violence
Vertigo-- moving on after retirement
Lawrence of Arabia-- starting over in a totally foreign land
The Mechanic-- Bronson's character trying to leave his profession
Total Recall-- getting a whole new life

On the dramatic side:

Under the Tuscan Sun
I Dreamed of Africa
Beyond Rangoon
The Beach
Alice Doesn't Live Here Anymore
Tumbleweeds
At Play in the Fields of the Lord
Witness
Seven Years in Tibet
The Last Samurai
Dances with Wolves

And on the comedic side:

Doc Hollywood
Baby Boom
Lost in America
Cheaper By the Dozen
Crocodile Dundee
The Beverly Hillbillies
Moscow on the Hudson
Volunteers
Air America
Being There
Pleasantville
Elf

Star Wars A New Hope. Both Luke and especially Leia have their homes devastated and have to move on.

what it this "star wars" you speak of?

Defending your Life - A humorous take from Albert brooks on the afterlife.

good will hunting

Moving

I wish they'd release this one on dvd.