Of recent Broadway plays, I think War Horse would be very challenging for anybody without the resources that Lincoln Center has. The horses are integral to the piece but don't have any lines, so you have to find some way of making them come alive with limited resources and budget. I am having trouble envisioning how a community theater could do this show without having it seem silly (which would be counter to the whole piece). The play also has a large cast, and has songs that have to be played and rehearsed as well, so it's also a bit of a budget-breaker.
I do not know when the rights were released (the tour finished pretty recently), but it will be interesting to see what regional productions are like (and how many there are -- this could be one of the least-produced Tony winners for Best Play in recent memory).
"What was the name of that cheese that I like?"
"you can't run away forever...but there's nothing wrong with getting a good head start"
"well I hope and I pray, that maybe someday, you'll walk in the room with my heart"