No idea. I just know that, of the established ones, BoM & [A N Other, probably Wicked] are never knocked down in price. I presume due to high sales. Tickets are available, I imagine, but just not from the TKTS places that everyone seems to go to (if they can be arsed to queue). I don't suppose...
Might want to try and book before you go. It's one of only two Broadway shows that they never discount tickets for (can't remember what the other one is- maybe Wicked?) so you won't pick up anything cheap at the TKTS booth last minute, for example.
I've never been in baseball season so have always missed out on the games, but I did go to the NYY Steak place :) Yeah, I realise it's probably like going to a Man United themed restaurant here, but my god, the steak was epic, and I'm not usually much of a red meat eater.
I stayed here in December. It was ace http://www.tripadvisor.co.uk/Hotel_Review-g60763-d5550873-Reviews-Archer_Hotel_New_York-New_York_City_New_York.html
Another vote for the High Line. Free, and a lovely way to while away an hour or two, and if you walk from north to south, you end up near...