I bought a toilet caddy from better living(Toilet Paper Caddies | Toilet Tissue Stands | Better Living). The toilet caddy product that I bought was Toilet valet. Toilet valet is very convenient. It looks elegant. You can store three rolls toilet papers at a time and it has a separate rack for storing magazines too. It is a chrome toilet valet and costs about $35. Better living offers a wide range of such caddies.
We attached ours to inside base cabinet door. Because the center panel of the door is so thin, I found a piece of wood flooring that kinda matches the cabinet stain. I then screwed it to the inside of the cabinet door frame, then screwed the Tp holder to the flooring strip.
It works great, it's about the same reach as the countertop but it's hidden. You just have consider what you have in the cabinet when locating where you want place the Tp mount.