Where do these stairs lead to?

[tufguy]

1) Where do these stairs lead to?

2) Where do these stairs go to?

Is the first one correct?

Do we use the same structure for ladders?

 

[Flamenco1]

1) Where do these stairs lead to? There is nothing wrong with that question. You could also say "this staircase..." or "this flight of stairs ..."
2) Where do these stairs go to? Also good. But possibly better, "Where do these stairs go?"
Is the first one correct? Yes.
We use the same structure for ladders? No (although there might be exceptions).

It is normally obvious, visually, where a ladder goes. You might say, "Why is that ladder there?" Of course, if the ladder goes to a hatch or trap door then you might use the verb "to go", but I'd normally refer to the hatch rather than the ladder.

 

[Yankee]

1) Where do these stairs lead to?

2) Where do these stairs go to?

Is the first one correct?

Do we use the same structure for ladders?

As a linguistic purist (when convenient) I would prefer not to end the question with "to". Rather, "Where do these stairs lead?" and "Where do these stairs go"?

 

[Tarheel]

Maybe it's just me, but I wouldn't say, "Where do these stairs go?" That's because stairs don't go anywhere.

It's rather an odd question anyhow, isn't it? You take stairs to the next level -- either up or down.

 

[Tdol]

Given that the choices are limited, you could ask what these stairs lead to (a bathroom, the attic, etc.)