How about the relatively recent but definitely trad-sounding "Come Fare Away" from Jean Ritchie (aka KyTrad on the 'Cat)? As upbeat an immigration song as any out there.
Molly, come fare away,
Come fare away with me.
There's and island of dreams
Over the (rolling?) sea... (don't have the recording here at work.)
And in the thread cited above is one about returning home to Ireland (where more people are arriving than leaving in recent years, for the first time in 800 or so years), and "Sweet Enniskillen" about recalling the sweet memories of the old home but knowing this is really home now.
The last verse mentions
"I know I never thought that I'd fit in here
In this place of so much bustle, that rattlin' subway train,
But so many arms and doors have opened for me,
And those arms have wrapped around me, so here I will remain."
Ed Miller also does a couple of good ones about the emigrant (now immigrant) and the perpetual balance between loving the old and the new. (OK, he's a Scot, but they are great songs anyway.) One is called At Home Among the Exiles. And the fantasic line, "My only homeland is six feet high. For its independence I would die."
Drop me a note if you want words, links, recordings etc.
And there is "John Williams," about an Irishman who was thrilled to be emigrating to NY, saying good-bye to "the peelers and the landlords and the risings of the moon." This song has a "kick" at the end if you do not know it. (He is traveling near the turn of the last century, to build a new life with his new wife, in a great new land where he can work to make his dreams come true; he is so glad to be traveling on a big ship, the finest ever built; they say that naught can sink her....)