I like "the classics" for the 4th, myself.

Some ideas:

Oh Susannah

Shenandoah

In the Good Old Summertime

However, most people no longer know the words to these.

I liked OldHippie's suggestion. To add THAT list:

Oh Freedom (you know, Pete's version)

Tom Paxton's Born on the 4th of July

Ani di Franco's Independence Day

Sure, that'll get you started well enough. Not a soul in your audience will recognize the songs, but at least you'll be sangin' on theme!