You're ready to move beyond the basics--what next?
Learn how to play barre chords
Barre chords are chords in that involve using one finger, usually your index finger, to press down two or more strings on a single fret. Here's a good lesson on the Ukulele Hunt site that will help you learn how to play barre chords.
Learn a few more more strumming patterns
This video by Brett McQueen of Ukulele Tricks shows you how to play five strumming patterns.
Buy a better ukulele
If you started with an inexpensive ukulele, consider upgrading to a better quality ukulele. I started with a cheap soprano ukulele, but after a year I bought a better quality concert-size ukulele with a richer and fuller sound. (See my contact page for a picture of my Mainland uke.) I improved rapidly with my new ukulele. Ukulele Hunt has a ukulele buying guide, which may be a good place to start. I'd also check out the forum on the Ukulele Underground website, where you'll find lots of discussion about different types of ukuleles (I learned about Mainland ukuleles on the forum).
It helps to listen to yourself play a song. I use the free Smart Voice app on my Android smartphone but there are many similar apps. You won't always like what you hear but this will spur you on to improve.
Learn how to read ukulele tab and play fingerstyle songs
Tab is a way of notating ukulele and guitar music that's easy to learn for those who can't read standard musical notation. With tab, you can progress beyond just strumming chords. You'll be able to learn to play melodies, fingerstyle songs, etc. Here's a good lesson on Ukulele Hunt about how to read tab. See my blog for examples of fingerstyle songs.