The best of the whole universe have absolutely nothing to do with adventures, which is weird given the premise.
In TNG, it's Chain of Command (There are 4 lights.), Darmok (the analogy language people), Tapestry (Picard's It's A Wonderful Life), The Inner Light (Picard lives a lifetime schtick), the Data philosophical stuff, etc.
In DS9, it's Sisko being a frustrated 1950s scifi writer, the one where Jake lives a life trying to save Sisko, the meta Tribble thing, Garak's character arc, etc.
The concept is hokey, but it's just a vehicle to get to the good stuff.