The Lying Earth

You'll get this task from Minister Clarke during the main quest, 'The City and the Stars'. He'll ask you to snoop around the HHC building and use Chairman Rockwell's terminal to send some data back to Earth.

To get into Chairman Rockwell's estate, you'll need to pick a locked side door, which requires a Lockpick skill of 60. If you have a UDL ID Cartridge, it can make this easier by providing cover. You can also get the Minister's Estate Key from Guard Mayfield in Billingsly's House of Inebriation if you give him three Spectrum Vodkas.

Next, you need to reach the HHC building. You'll encounter a restricted zone at the gate to the Acropolis District. You can get past this by talking to Guard Stallworth and passing a Persuade check (40) or bribing her for about 2,000 Bit. Alternatively, you can try a Lie check (65). If those fail, you can sneak through the maintenance tunnels by picking a locked door (Lockpick 60), or use a UDL ID Cartridge to walk right through.

Once inside the HHC building, head south past the receptionist and go to the security checkpoint. Guard Bachmeyer will try to stop you, but just show him the credentials Minister Clarke gave you. Then, ride the elevator up.