Objectives: Complete side quests.
Believe it or not, you can complete the game without entering this area at all, although you'll probably want to take a look, as many of the side quests for this planet require you to visit the Sandral grounds at some point. Even if you're not the side-questing sort, you may still want to pay a visit to the Crystal Cave in the eastern part of this area to pick up a large number of crystals for your lightsabers.
Objectives: Discover what happened to Revan and Malak
Speak to the slave droid in the main room here for a long conversation about what exactly these ruins are. Eventually, the droid will come around to the point; in order to discover what exactly Revan and Malak were up to, you'll need to prove yourself worthy to enter the Builder's construction by undergoing two tests, one to the east, one to the west.
Each area consists of an ancient computer terminal, protected by a guardian droid. These droids are highly resistant to most forms of damage, including energy damage, so your lightsaber won't help you very much. If Bastila or your PC has learned stun droid, then this would be an ideal place to use it; you can even use this power to hold the droid in place while your other party members pelt it with ion grenades. Whip out an ion rifle or ion blaster to finish them off, then access the terminal. It will be garbled at first, but if you talk to it, then insert your datapad, then talk to it again, you'll get an interface in galactic basic. Each will ask you to choose three options from a group of six, based on which types of worlds are more likely to bring death (Barren, Volcanic, and Desert) or life (Arboreal, Oceanic, and Grassland). Access both of the terminals to unlock the passage leading deeper into the ruins.
Once you possess the Star Map, return to the Jedi Council. You'll gain a new party member, Juhani, assuming you didn't punch her ticket back in the grove, and be granted permission to leave Dantooine. Head back to the Ebon Hawk, and take a little time to talk to all of your party members to get up to snuff on their personal journal entries--some of these will open up side quests later on, so it's worth getting up to date while you have a bit of downtime. Juhani, Bastila, and Carth will each have new responses to your inquiries at this point, so make sure you rap with each of them before shuttling off to the next planet. You can choose any of the four; you'll need to visit all of them eventually. Due to its alphabetical preeminence, and because Wookiees are cool, we'll head to Kashyykk first.