You'll find one portrait in the downstairs hall, three in the parlor, and three in the upstairs hall.

In the downstairs hall, Beauregard Thornton is on the right wall across from the door to the tool room.

In the parlor, Jeb Thornton and Sarah Emma Wakeman are over the fireplace, and Hiriam Thornton is on the far wall.

In the upstairs hall, Franklin Thornton is on the right (or he will be as soon as you replace the missing painting) --

What do I do with the empty frame?

-- Jackson Thornton is on the landing next to the sleeping bag, and Mariana Thornton is on the hall to the locked door.