I did not see any official suggestion post, so if there is please point me to it.. 
There are a few things playing GCII, that bugged me, and i think a tweak could really make the game that much better.
Planets, While there are lots of different types of planets, they really all boil down to being the same. they just have different numbers of build-able spots, or tile bonuses.
Id like to see this improved.. Perhaps add elements, A small high gravity world, could have a much higher iron content, giving bonuses to ship building, Other planets could lean into better population happiness. A resource rich world could add a economic bonus. Perhaps controlling resources, or groups of resources on planets could lead to other bonuses empire wide. Metals, gasses, ect..
Mining Planets. instead of just mining random asteroids, or space resources, why not add resources to planets to mine for bonuses. Say a planet is rich in a certain ore, but is hard to mine, and toxic.. populations would need to be shipped in to continue to mine, Having to haul people off the planet and replace could lead to interesting good/evil game play.
to further go along that theme, these mining planets could have their resources shipped through trade to your own planets to boost things like moral, growth, shipbuilding, ext.. You could also trade these resources with other races. The idea being, that collecting resources, or groups of resources could lead to larger nation wide, boosts to certain things.
Mining Gas giants, and/or habitable moons. the idea is kind of self explanatory. The resources would be part of the mining aspects of the game, while the moons, could add more planets to colonize, but be different in some aspects. Say you are mining a gas giant, but it has a moon, setting up a station their could lead to letting you trade to planets farther away, Or improve the mining rates.
Basically the idea's are to make worlds a bit more unique, and reasons why you would want to improve one world, over an other. As it is now, outside of location, there is really not much difference between worlds for the most part.
engines/life support.. to me this is a huge one, Especially on smaller maps, the need for faster engines, or life support can be completely useless, Decreasing the base range would make life support upgrades, or just adding more mean something. Verse just pile all the weapons you can, and hope for the best.
Perhaps engine speed have more effect, outside of how fast it moves per turn. Not sure how this could be done, But even a planet inside your own space, if far enough away, perhaps it would need a better engine just to reach the planet. Some sort of distance association with engines should be added.
Id also like to see the colony rush slowed a bit, having many more planets is often the biggest factor. Out expanding is almost always better, But if costs for more planets, more ships, more territory scaled a bit differently, perhaps a smaller empire might be more viable. It could also lead to more planets being available late game for colonization, verse just fighting over them.
these are just some basic thoughts.. things that have crossed my mind while playing..
one last thing, I really hope there is some sort of editor, added with the game.. A way to make your own campaign, Or tweak what's there could be fun. I often think about how the planetary events, when you colonize and make a choice, or the random pop up ones. I would love to see that expanded or the ability to expand it myself