Upper body, adding something for the back would be good, but IMO that's the most challenging area to work without equipment.

Yup. If you have a sturdy table, I'd suggest "horizontal pull-ups"/inverted rows.

Or there's this nifty unsupported row.

Or try pushups on your knees, or against the wall.

And check this out:

http://www.stumptuous.com/mistressing-the-pushup

All the things you're learning from planks about holding your torso stable will really help with inverted rows and push-ups.