There's a bunch of options for this task, but combining the three wheel stair-climbing dolly with the self-balancing hoverboard/segway seems like the easiest.
you don't need legs to climb stairs, you can have a rotating mechanism with different rows of wheels that have good enough grip, maybe an extruding stick to lift the whole robot up and the wheels move forward... would take a lot fewer joints than pair of legs probably.
If this was awesome, we would have it on wheelchairs. We very rarely do. Stairs are built for legs.