How can I create temporary storage space in a motel room?

A few plastic shoe boxes with lids can be stacked in a corner. One with utensils, another with spices, etc.

See thru plastic bins from any discount store.

Not sure the dimensions of your room, furniture already there, or whether there's a big open space under the vanity in the bathroom and such, but here are a few options that won't take a lot of space and that will be useful when you move on from the motel:

over the door shoe pockets can hold things like spices, snacks, small packages of things like rice, and condiments. You might have to put it on the outside of the bathroom door since many closets have sliding doors

a second over the door shoe pocket thing could go inside the bathroom for holding stuff you use regularly - makeup, shampoo, whatever

a small wire shelf (like is sold for shoe storage) could tuck into a corner or even sit on top of a desk or dresser to hold dishes, pans, food, etc.

plastic drawers on wheels can tuck away in a closet or next to the bed or even under a desk. A cheap silverware sorter in the top drawer allows you to use real utensils (pick them up at a thrift store and wash them well if they're too costly elsewhere). Lower drawers would be great for things like kitchen towels. The top could hold a drying mat and dish drainer.

Cigar boxes are often sold very cheaply at tobacco/smoke shops. They are an attractive way to store stuff on top of desks or dressers without everything being visible.

When my daughter had a tiny kitchen, I gave her one of those plastic dressers like you can buy at places like Walmart to keep all her utensils, silverware etc.

Thanks ya'll these are all great ideas ,I look forward to trying .