I don't know of anything analogous to codeschool and the like, and I am having a hard time imagining such a thing. Design is in many ways comprable to coding. It encompasses many different skill sets and disciplines. Designers are like programmers in that they must research, understand a problem, visualize, iterate, organize, implement, optimize, etc etc etc. Design can be hugely complex or rather simple, just like coding.
I am not that familiar with the offerings of codecademy etc, but I tend to doubt that anything taught there can replace experience and serious study of algorithms and patterns. So while I suppose there could be a site teaching about fundamentals of composition, line, form, color, typography, etc, I'd think you'd be better off reading a book on those than anything else. Any exercise you would do would have to be evaluated algorithmically, which seems very hard judging by the subjective nature of design.
Like coding most growth in design happens through actually doing it. This means developing drawing skills, rapid prototyping skills, and most importantly your eye. I don't think any of this can be adequately taught through an interactive website. My suggestion to you would be to simply begin designing.
Hope that helps...
