Google "free ukulele songbook"
You will find about 30
free songbooks available for download that have been posted by ukulele clubs from all over the world. The vast majority of them are very simple songs to learn and play. Many of these collections have simplified versions of more difficult songs for beginners.
Depending on your style as a uke player there are other sources as well that are also absolutely free. I'm a singer/strummer (although the singing is pretty awful). One of the things I sussed straight off is that a C on a piano is pretty much the exact same sound as a C on a ukulele. So, as a singer strummer I find some usable music from the music section at my local library.
Piano sheet music is written with a heck of a lot of information on it. A lot of it has chord notations for accompanying instruments written above the piano music. These are pretty much exactly what you want for strumming on a ukulele. Virtually every popular music collection and screen/stage musical ever performed has sheet music written like this. You can even find it on piano music for Disney and Pixar cartoons. For instance, you can get the book for Lion King, and have all the chords to play any song in that movie...
To give you an idea of what to look for, these are the chords to Camelot, from the musical Camelot. I've circled the first line of chords. The attachment isn't very large for some reason, but it's big enough to show you what to look for.
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Once you figure out that a C is a C is a C, you can use almost any sheet music that has a chord notation on it for strumming. I don't do any of the fancy picking that a lot of people do, but I suspect that if they could read piano music, they would be able to use it for that style of uke playing too.
