Old furniture often has it's own imperfections, some things are considered character and others well are kind of gross. For Example the inside of a drawer that has had who knows what in it?!
I have an easy solution for you!
Paint your drawers, and if you want to go a bit further add a little character to them, like stripes! Instead of an ugly disgusting drawer you now have a new drawer full of character!
To paint the inside of a drawer is it important your prep correctly:
First make sure everything is cleaned out of them.
Once they are cleaned and smooth use an Oil Base Primer to seal any stains into the wood.
This will also eliminate any bleed through when you paint.
Then add your color of choice, and a fun design if desired!