Two hinge mounting strategies, on a cardboard and cardstock prototype.

Left: Mounting the hinges under the tabletop. Less visible, and keeps the tabletop propped up. This takes up more space in the room, but also provides more space to spread out puzzle pieces. This could also ultimately be modified to be load-bearing.

Right: Mounting the hinges on the sides of the table, and above the tabletop. This is more visible, and allows the tabletop to fold fully closed. This leaves less table space, and a more compact table.

Ultimately, because the table is so small (smaller than the coffee table it will be replacing in my apartment), I decided to go with the configuration on the left.