I've always just kept mine in my utensil drawer. For me, the question is how to store my pizza peel and trays. One of these days, I need to retrofit one of my upper cabinets with vertical dividers... 18" cabinets, 17" pizza trays :) then perhaps the pizza peel simply hanging on the wall somewhere?

oldbattobe: you have my drawer!! I recognize everything in it. When I can't' find something that is my hope drawer. I like to rattel through it. Wouldn't change a thing.

In my laundry room I have magnetic strips that are usually used for knives in the kitchen. I put different size screw drivers and such on them. I can see what I need for DIY projects. You can also put candle putty around it or get a big enough envelope. You have something in your home or wait for a container to come into your life. Mine is in a drawer too.

Pizza cutter will be too tall to store upright.
I put mine in a made right 6x9 inch bin.
I do have other items in the bin but keep the blade against the bin wall. On the road but will try to post.

Why not just protect the blade instead? A cut clean sponge with a slot in it, a piece of foam, whatever, and a rubber band.

How about a cloth drawstring satchel, drop it in, pull the bag shut. It can safely go in any drawer you want.

Cut up a gift box into 2 squares that are each large enough to cover the blade and tape/staple them together on 3 sides. It will make a nice blade guard. I've done the same thing with exacto knives and my meat cleaver.

I keep my pizza cutter in my knife drawer. Here's a picture of it. It's in the upper left corner with the blade facing the corner, safely out of the way.