Between impending-50th-anniversary talk and that recent thread grumbling about the way Enterprise ended, this seems to have circled back in my thoughts again.
Personally, I would take what I like about the new films (the hectic pacing, the heroically capable but sometimes conflicted crew, and the KABOOM) and apply it to new stories. Crank up the Weird Level of on-screen and in-crew aliens to at least the level of modern Doctor Who. That kind of thing.
Also, Lena Headey as the Captain.