When staying in a hotel room, there is NEVER enough storage space, and usually no drawers in the bathroom. I found that a simple plastic “mesh” basket is the trick. Usually you can find them in the toy area with sand box toys, or sometimes in back-to-school sales for dorm shower supplies. I placed it on the small bathroom counter and stood up the items that I knew I would use most frequently (toothbrush and paste, contact solution, combs, hair products, etc). Those items that I used less frequently I kept in my toiletries bag under the counter. I had a much easier time finding what I needed, and there was still a small amount of available counter space.
The first thing I unpack at a hotel is the hand sanitizer, This trip, I also brought Lysol spray and air freshener since we had four people and only one toilet.