Small damaged area on wood floor

Q: We are purchasing a house. There are two areas in the kitchen that look like the the finish has come off the hardwood floors. It appears to be a little water damage / high traffic areas. Someone suggested maybe spot sanding and putting a water base over it, that there might be slight discoloration for a while, but it should work just fine.

Is this the best solution or is it better to replace the floor boards and restain, or replace all the hardwood in the main room? The spots are about 2 x 2 feet.

A: If the finish has come off the floor, it puts a question in my mind as to the finish in general over the rest of the floor. My view would be to have the entire room sanded and finished again, using top quality products and techniques.