I found a lot of easy songs on Youtube when I first started out. Just search "easy ukulele songs" and you will find many beginner tutorials. Also, have you watched Aldrine's beginner videos on UU?
Another useful tip I found when I was new,
was to google 'Name Of Song Chords'.The
pages that this threw up were generally
guitar chords,but a C chord is a C chord
as we all know! So if you get the words
and the chords,its easy enough to use the
chords (if you know them) or add the chords
yourself on your computer or by hand!
Worked for me,and for many of my friends.
YouTube has lots of tutorials with easy songs that show chords ands STRUM patterns ( the hardest thing for me ) Aaron from Hawaii Music Supply and a man called ukulele Mike are just 2 of your many choices! I hope you have fun with it!
Just about every early-era classic country song from the 50's-70's is fairly simple and easy, usually with only 3 chords.
This site is awesome and has the lyrics and chords written out nice and clearly: http://www.classic-country-song-lyrics.com/
I bet you've already seen this, but Ukulele Hunt has an excellent beginners (free) ebook. Along with a bunch of other tips, he has a list of easy first songs to learn. Ring of fire is especially fun.
Try using "The Daily Ukulele" book. amazon has it pretty cheaply. Also ukester Brown has a great site with downloadable songs and videos for every one of you are not sure of the melody.
Start off learning with the basics in foundation...Rhythm and Timing..since you know nursery rhymes, it would be easier....http://www.baby-patch.com/guitar.html