Not sure if this is exploration exactly, but I'd like to see a film centered around a first contact situation. The crew encounters a new species while exploring, perhaps stumbling into an area protected by a territorial race (as has happened many times), and initially there is conflict, and the new race wants to eliminate the "invaders" as they perceive the Enterprise and her crew. Then perhaps there comes an opportunity for our heroes to help them in some way (again as seen in many episodes) and so the beginnings of a relationship between the Federation and these people are formed. I think it might be more interesting if the new aliens were far advanced in some way, either technologically, or academically, etc.
Or, as an alternate scenario, while exploring a new region of space our heroes could encounter some sort of natural force they're unfamiliar with and it poses a direct threat, and they must figure it out and save themselves.
Just my thoughts on a possible scenario based on exploration. I think lots of great stories could come out of them exploring new regions of space.
Not sure if this is what you mean or not, but this should prove an interesting thread!