I'd also like to share my feedback. Ok, I'm just going to make this as easy to picture as possible for my ideas and for areas that can be improved.
First part that needs adjustments: I think that the boundaries for each planet's area of cultural influence should work exactly like in Civilization V where the culture expands the borders. Star bases should only be allowed to be built in within your borders of that specific planet for that specific planet as well.
Second suggestion: I would suggest to create a tile system on the planet that works a lot like Civilization V (once again brilliant design in a brilliant game.) There should be values for gold and production and food in each tile. I would also like to see the asteroids have special precious metals and have different capabilities from having these asteroids. Also Galactic Wonders near by to planets that can add special stats to planets and that would give them tactical advantages for colonizing that planet.
Third Suggestion: I would also like to see A Tech Tree for each of the 4 Main Branches of Research. Something that gives you a more tactical view of what you aiming to gain scientifically.
Fourth Suggestion: I really like the star dust and nebula effects and how they change the positive and negative effects of being in that area. Would like to see more areas with positive stats like defensive bonuses or stealth or attack bonuses or even movement bonuses.
Fifth Suggestion: I would also like to see the special buildings like the Benevolent Specialty Structure should have a lower incremental value for how much benevolence you get from it each turn. +5 is too much per turn. Also there should be a cultural building that increases in level gradually slower and slower as it increases your planet's borders and areas of influence. Would also like to see a just a bit smaller area of initial Planetary borders when you first colonize a planet.
Sixth Suggestion: Colony ships should be able to go a lot farther into space and make the research for Logistics/Space Travel Distance A lot more gradual and cost less research points. ( Or in my opinion Seriously Scrap the Limitations to how far a ship can travel because it messes with the Cultural borders of planets.) This game should be a lot more like Civ 5 with land borders vs planet borders. The border system should work the same. It shouldn't have limitations as to how far a space ship can go. It kinda ruins the whole point of The Civ Series. This is just my opinion but in reality, The game play would work a lot like Civ 5 multiplayer gameplay and everyone loves that games for how smooth it plays strategically. It makes the game a lot more easy to play in and a lot less complicated. Other than that, if you really want to keep it in the game then the map sizes will have to correspond to how much logistics changes in each map size and they would have to work differently. As well as Special resources planet side from cultural borders would have to also work in conjunction with those rules.
In my honest opinion, this game should have a ton of qualities that The Civ Game Series from Civ 4 and 5. This game would be frigin amazing if it keeps the same game functions from Civilization V. No doubt in my mind would I be satisfied every time I played the game.