access to facilities are controlled in 3 ways.
1.open to all - which is at is says open to everyone
2. open to faction - only open to members in the faction that owns it.
3. crewlist - each character are added to the facilities crewlist and can enter. see it like you got the keys if you are on crewlist.
There's not really much to do on the ground. Inside facilities, all you can do is walk around them, and you don't even get XP for that. (: Best just to wander around the city until your faction can pick you up and put you to work.