"Beyond the "official" numbers quoted, I personally felt a real vibe of going forth into the unknown in the early seasons of TNG - the great unexplored mass of the galaxy! I don't know, somewhere around season three, the show seemed to lose that sense of "wonder", to the detriment of the programme IMHO."
I felt the vibe going forth into the unknown was pretty much absent from TNG onward. TNG had its merits in other areas, but the whole first contact thing was rarely done. They could be non-aligned worlds, and it could have been the first time the alien species was shown, but the world was already known. That would be disclosed in the initial captain's log exposition. So right from the get go you lose all the mystery of what it is they're coming across.
(BTW, I think that's why Darmok is one of the best episodes because at least you have a species that is truly alien and they can't even communicate properly.)
They tried to recover this vibe in Voyager, but in the context of an "accident", almost like Starfleet no longer had a true mission to explore the rim. Then once there, they brought in familiar faces like Q and the Borg.
By the time Enterprise rolled around I had pretty much given up.