One thing that has bugged me a bit about the exploration spaces is that they are still unexplored. Especially the first one you are told to go to that's right next to the Sol system. It doesn't make much sense that the region of space right next to Sol is still unexplored. So here's a simple solution: wormholes.
Have wormholes show up that have a stable point in known space, but a variable point in unexplored space. The backstory would say the variable point moves every few days, giving plenty of time to get back to the wormhole before it moves again, and giving a reason that all these systems are still unexplored. It shouldn't be too technically difficult to set this up, just make it similar to the transwarp conduits that we have in the game now. Because the variable point only moves every few days, there's no need for anything special to be done on the other side.
You fly from from city A to city B. At 900 Km/h, on 10.000m you don't see much of the countryside below you. You see it is green and it is there.
If you walk, instead of flying you will see all the small details and explore everything. However the time to get to the other city would take months instead of hours.
Starships flying at high warp are like airplanes. They notice that there is a star here and a nebula there, but they don't really know if the star has planets or life. Finally, there is a good chance that the long range scanners completely miss floating debris or smaller planetary bodies. And if noone travels in one particular direction (because Vulcan and Risa is in the other way) then chances are good that it will remain uncharted.
Space is vast and flying arund low speed to discover all the small detials would take forever. So the area around bigger systems are well charted. But space between them are totally uncharted.
Which means, I don't have any problem with current way to enter the exploration area.