There should probably be different stages or phases of the game, one where exploration and development for the sake of exploration is key, another where interaction and development for the sake of competition is key, another where you're threatened by war and have to fight (or you're the one doing the threatening). This means that the micromanaging would dissappear should different phases have different amounts of automation, so that you can list your priorities on a world and let the AI deal with it. Then just say "all colonies with >50p production that have build missile bases and fighter garrisons - build a warship", and not worry about every single world.
There being things left to explore even tho you have the whole galaxy "explored" is important. What if there's something that can create new worlds, or even new star systems? Random changes (with no status message/galactic news report saying it changed climate from ocean to terrain because X) that change the terrain or add stuff could be cool. An ancient civ that camouflaged its worlds as gas giants would also be cool, as would invaders from another galaxy (and/or wherever the Antarans in MoO2 came from).
You'd still want to know the most evident things of a planet just by entering the system, so what are, realistically evident? Color, spectrum... number. Earth has currently detected over 200 planets outside our own solar system, and from a distance found signs of water on some (whether or not this checks out will have to wait until we get there... which won't be anytime soon, I fear). You would probably see gas giants from other solar systems, given the science to do so - but even when you enter a solar system, you can't see how much of what and in what forms it exists, you'd have to get far closer to explore a planet to learn it's climate (in relative detail), how much ppl it supports, et cetera. Say, stay a turn or two if there's any planets of the right size to check out.
Anything on, or in, these planets would be difficult to find. Ruins, other civs that don't have anything in orbit (or a glowing urbanization display (at night) such as the one our world has (or is) at night), mineral bonuses, stuff like that.
Also, what if, at a later stage, space battles leave a lot of scrap behind, that other players can come and salvage. There could just as well be those around in space at the beginning of the game (unless enforcing some kind of young-life/civ creationism or something on the game). Regardless, ruins on a world could contain not only a resource bonus, but a defensive one as well. Just think of what Atlantis can do in Stargate Atlantis. Aside from giving a research and possible industrial bonus, why not include the feature to learn how to use, although not (at first) reproduce the weapons and shield technology present in old advanced cities?
Derelict scouts from other worlds where the crew went nuts and killed themlseves would also be interesting... or unmanned ones whose computer froze or crashed.
Just, what could there be at the end of the game worth exploring? Maybe a competition to capture comets for the resources they provide in terraforming worlds (they're mostly some kind of ice, I hear). Crashing a planet into another is a little too ambitious, but igniting a gas giant far from the sun to terraform its moons isn't a new idea to scifi.
Okay, back to exploring... Maybe the center of the galaxy cools down enough to form new systems in there? Maybe there's a way of manipulating the sun of any specific solar system to terraform its planets.
Look, I got stuck on finding worlds to colonise and once again returned to terraforming. But building a generic terraforming device shouldn't be an option for every world. The worlds are different, as are their needs. So aside from shipping water from an Ocean world to a Desert world, we could need some options on that.
But now, back to exploring. Some spatial ripple could produce new solar systems, black holes might be manipulated into becoming white ones and spew out a cloud of matter that over a great number of turns may form new systems.
Besides, if there's some meter tracking the age of stars (which I, a young-Earth creationist, would likely find quasiscientific), new solar systems could provide elements not present in older ones. Different stars likely have different planets, so whether or not the meter is tracking age or just type, the stars could change type, given enough time (some kind of gradual change (or one when there's no-one there), not a GNN headline: "Generica has changed from red to yellow and now contains two Terran worlds etc").
If the starlanes would be connected to a planet (as in a fixed position in the system), rather than to a solar system as a whole, you'd go from, say, Earth to Generica II, but still need time to go from Generica II to Generica III which might be colonizable, given the time to explore it and the rest of the system. That makes detailed exploration take more time, sure. Maybe that's not a particularily good idea.
Let's consider it anyway. You enter a system, you get the sensor report that there are six planets there. You're on #2, and it's radiated. Your sensor tell you #4 might be terran. You get closer. You get the sensor report on #3 (or not, they can be on the other side of the sun, so whether or not you get one should probably be random) it's desert. You get to #4. It's terran. It doesn't belong to anyone yet. You colonize it. Next turn, you learn it has dangerous wildlife. Construction is halted to build defenses. Two turns later, you learn the planet is mineral rich. Nice. It doesn't help you yet, you need to build a mine befopre it's of any good to you. Four turns later, you find it's atmosphere causes some medical problems. The scientists on the planet would fix that in four turns, so you add some to get it down to three turns. An enemy arrives in the system, through a star lane connected to planet #6. You rush some defenses through production. You just saved your colony.
At a later stage, this is too much micro-managing, but when it's your first colony, it's fun. Or, it could be. I dunno.

It's exploration, albeit on a smaller level.
At a far later stage, you'd enter a colony and get most info from your superior sensors... But some remain unknown. Plus then it could be more of a way to find the best resources to terraform with, finding a dry but otherwise good planet to terraform by using water from a nearby icy moon or meteor or ocean world or whatever. Or dump asteroids into an ocean world. Or crash meteors into a radiated to give it more atmosphere and more material to synthesize ozone from. Then the exploration and strategy lies in finding the best resources to use.
Whoa, I have a lot of ideas. Or a difficulty phrasing them any shorter than this.