To find out what stairs you can currently challenge someone in, first go to the Main Stairs Page, then click on "Show your stairs only" link. The ones in BOLD are ones you can make a challenge in. .
speaking of a lot of draws, i know this is far-fetched, but it's happened to me so much that i'm compelled to ask: there isn't some bug or something in the stair code that greatly increases the likeihood of a two-game match ending in a draw, is there? i don't think i've played a single two-game match in any stair that hasn't ended in a draw, and when i commented on that just now to an opponent (with whom i'd just drawn a two-game match), he said he's seen the same thing. whole lotta drawin' goin' on...