I suppose it's not full galactic exploration I'm looking for but moreso the ability to stake out one's claim in some isolated area or to still be able to find useful planets after the galaxy has aged.
Also- Is it time or tick-based, or can you fly around doing stuff on your own time?
Being able to stake a claim is easy;get a biodome, find a planet, place biodome, take a few dozen colonists and drop them off, they'll reproduce quickly if its hospiteble, if not they'll slowly multiply. give them organics and anaerobes to boost reproducion, oil and meds to boost morale. Earthlike planets produce organics more than others whch makes it easier to get lots of workers/taxpayers quickly.
The hard part is keeping them after its aged awhile, unless you go way out from Sol or other Starbases (making a colony near the one or two pirate Starbases is not a good idea if you have positive Rep.). if you set a colony to Corporate instead of Personal other Corp members can help supply stuff and set up more defenses.
You can do stuff on your on time, only limits is how much money your character has (you lose it and all your cargo when blown up unless its in the bank, but can go and pick it back up if your attacker didn't grab it), and warp fuel, which is generated at a specific rate per min. You start with at least 2000 fuel, the cap is 5K. (the average is .50/min; I believe Pirate's Heyday is set at .67/min or so)