My favorite problem is always to design a game (though, to be fair, game design is the main reason I fell in love with programming in the first place). The app does have a nice Python game tutorial, try following that along and see if you can improve or change the game!
Another challenge: grab text from a website, parse it so you get only relevant information, and output that information in Pythonista. An easy example is take a look at a the Google "I'm feeling lucky" page and see what the result is.
And if you get that challenge down, you can take it a step further. Have the script visit a site with stocks or price ranges, and try to graph those prices in Python! This could be awesome if you're trying to built your own investment tools and want to apply your own algorithms to the graph. There's some good plot examples in the app to get you started on this.
Just some ideas! Have fun and ask yourself "what would I want my device to do, for me?" If it's not impossible then you can probably program it.