jtate,
Here's a suggestion if you want the bottom of the box to look good. If you use a forstner bit to predrill boxes, then make a slotted stick with handle to hold sandpaper and size the stick just below the bit size. Sand with the stick 'til you're satisfied with the finish. Then turn an insert to just fit the bottom of the box, and glue it in.
If you really want to blow someone's mind, then turn it of the same wood and grain orientation, then engrave or sign it before you glue it in the bottom. They'll wonder how in the world you did that. Especially on a tall box...