It looks like you couldn't even fit a tower over the toilet with storage above, and this bathroom is so small - I would go just outside the door in the living area on the common wall and use an armoire - pax from ikea would be the low end, something from pier one might be attractive but inexpensive, something from Room and Board quality you could keep for life - use the armoire and under the sink, use a caddy that you can pull out. There isn't room for anything inside this bath - best to leave the tile intact and store outside.

We have a very small washroom as well and use a tall hutch with glass shelves and drawers, which was purchased from Ikea. The example below is very narrow and may work. I have also transformed my linen cupboard to hold toilettries, so space under stink can be freed up for blow dryer, etc. We have an armoire in another room for the linens...this idea may help you as well. http://www.ikea.com/us/en/catalog/products/50245665/#/70245669

It doesn't look like you have enough space but here is an option that doesn't need to be drilled into the wall. This one is from Target. Hopefully something like this will fit.

I watched the video suggested by Monarch Sofas. Very cool German technology! I don't need anything like that, but it looks like fun to install. Too bad I don't have a 200 lb man who could test it by hanging from the towel rod.

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Wow thanks for the great suggestions everyone!

I'm not sure if there is any room on your floor other than behind the toilet. If so, you can try a shallow cabinet or shelf unit.

We set-up a small cart from IKEA on one side of the bathroom and are looking at getting a nice over the toilet storage unit. I'm still pushing for the no drill shelf but we'll see. I'll add some photos soon.

Command makes some great clear plastic containers in various sizes and also some decorative hooks that small wicker or fabric baskets could hang from.