There's an app called Adobe Ideas for iPad which I've gotten to know fairly well. It's free for both iPhone and iPad (I personally love the iPad version because I feel that it opens up so many more possibilities).
The app allows you to draw in different brush sizes, opacities, colors, etc., and it's all vector based. You can upload the designs to your Creative Cloud or email them to yourself and open the PDF in Adobe Illustrator to edit the vectors.
I love the app because it's so simple to use and understand even if you're a complete beginner. The default color palette works beautifully, opacities and sizes are incredibly easy to set, and the sharing options are all there (you can send your art to anyone regardless of them having the Adobe Ideas app, but all the vectors are still there if you choose to send the file to a computer).
Check it out and share your creations here!