I just bought my first digital piano (a Yamaha CLP-430) and am now looking for good headphones. Are there any particular features that should look for given the intended usage?
You may want to consider the distinction between open backed and closed backed headphones.
Open backed are usually considered to give better sound quality, and better bass response, but won't block any noise in the environment, and allow bleed-through if you end up recording via a microphone. Also, the fact that they allow air flow can make them more comfortable for long term wearing.
Closed back will provide better isolation from any external noise, and may serve you better if this isolation allows you to concentrate better.
Finally, make sure that they fit comfortably on your head.
For use with a piano I don't think it's particularly necessary to have good headphones. You want ones that can handle a good range of volume without the clarity being greatly affected, so you'd best avoid tinny little earbuds, but other than that you should be OK. One possible exception is if you're playing pieces that go extremely low on the keyboard; A0 is 27.5 Hz, so you'd need headphones that have a dynamic range that covers that. Most commonly you'll see 20 Hz - 20,000 Hz which is more than enough.