If you have a way to improve starbases, post it here. I've come up with the following ideas, but there are many ways to make starbases better. If you have one, or several, just say it here.
The first is what happens when you are done with the starbase. After an Influence base conquers everything in it's radius, what then? What about when fighting draws away from a military starbase? Some people say that starbases should be able to be 'towed' by other ships. That is a good idea, but there has to be restrictions. How can a tiny-class fighter or a small-class destroyer 'tow' a massive space station? The towing module should be about size 40. That way, smaller ships cannot tow. Larger ships would have less space available to weapons, support, sensors, defenses, and engines at the expense of being able to tow a starbase. And the speed should be extremely low- 1 parsec a turn.
The second solution to that problem is allowing range-increase improvements. A technology trail (maybe off of life support) should allow starbases to add modules that increase their range, similar to sensors. +1, +2, +3, and +4 might not seem like much, but when added together, you get a range increase of +10.
Next is espionage. I'd really like the option to place an agent on a starbase. The menu that shows all of the starbases' improvements would come up, and you could pick one to disable. What's an influence starbase without any influence improvements? Or a mining starbase with no mining modules? A second espionage idea would have other benefits. Agents would be able to do other things besides disabling modules. An agent could redirect a mining starbase to your empire instead of the enemy's. You'd be able to do similar things to other starbases.
Lastly, I think starbases shouldn't be destroyed in battle, that's just a waste. You should have the option to bring a transport, capture the starbase, gain the benefit it provides without destroying it.