Do you have measurements of the room? Do you have measurements of the furniture? Draw it out on graph paper or use an online tool and post it here. That would help everyone incl. you 'see' the dilemma.

Is this a hutch with two pieces? Bottom cabinet and shelves above?

You might be able to store the top and use the cabinet on the window wall.

It is very difficult to help without seeing pictures of the room or the item, a floor plan or knowing the size of the furniture.

Attached are 2 pictures of the room.

Nice dining room!

Your square table takes up a lot of floor space. If the hutch doesn't jut into the room too much I would center on the longest open wall space. My main concern would be the clearance around the table.

Why do you think you can't fit the hutch on the open walls?

Thank you! I just couldn't figure out which wall to place it.