If you're looking for some patriotic tunes to try you should check out the Ukulele Tips 'n' Tunes book from FMM. It's got You're A Grand Old Flag, America(My Country Tis of Thee), The Star Spangled Banner, Yankee Doodle, and America The Beautiful.
My favorite book at the moment is Ukulele Gems (from FMM again. No, I'm not a shill for them, they're just great books for the uke.)
I mentioned Heart and Soul before which I found in this book. I also discovered It's Been A Long, Long Time which is a great song to play on the uke. Others I'm practicing from this book are Ukulele Lady, Bye Bye Blues, Ain't She Sweet, All Of Me, and Sentimental Journey.
Sentimental Journey is a real finger twister for me but I'm starting to hear a LITTLE progress. This one will take a long time but could be worth it. I'd love to hear/see how others finger an Am7 (2433) which needs to alternate with (2033), maybe there is an easier way than what I'm using.
Have a great 4th and come out to Como on Wednesday if you can, I'll be down there 6-8pm or so.