Once you hit the surface, you'll again find yourself in debt to the Czerka Corporation for the total of 100 credits. You can convince the customs agent that you really don't owe him 100 credits, or just pay him off. Buy some bantha fodder from the merchant near the Ebon Hawk; you'll need some later on.
After that, you'll automatically be granted the galaxy side quest The Trouble With Gizka. If you're in a hurry to get rid of them, you'll need some gizka poison, which you can find at the merchant on the docking pad.
Objectives: Find the Starmap
Your first order of business here will be to acquire a hunting license, if only so that you can leave Anchorhead; the Czerka slugs that own the town refuse to let anyone without a license out of the gates, and that somewhat curtails your options on this planet.
Head to the Czerka office and ask about the possibility of obtaining a license. Unfortunately, they're no longer sold, so you'll have to take on a task before the protocol officer there grants you one. It seems that the Tuskan raiders have been attacking the Czerka's sandcrawlers, apparently out of anger at the technological intrusion into their land. Even I know that you don't violate the Prime Directive without taking your life into your own hands, but apparently the Czerka don't care all that much for Federation law. Anyhoo, the Czerka wants you to wipe them out...all of them. Go ahead and accept the quest; you'll immediately be granted a license, with the understanding that the Czerka will pay a bounty for each gaffi stick you bring back to them.
Once you leave the office, the Duros you saw inside earlier will grab you and ask you to exercise a little restraint in your dealings with the Tuskans. If you're heading down the path of iniquity, you can brush him off right now; otherwise, talk to him to learn of communication problems with the Tuskans that may be solved by a special droid available elsewhere in town.
Another place of interest is the swoop registration office, where you can speak to Motta the Hutt to pick up the Signing Nico side quest, or sign up for some races of your own.
Elsewhere, in the cantina, you'll be able to purchase some fine Pazaak cards from the bartender; he offers up two copies of each of the +/-2, +/-3, and +/-4 cards; this should be enough to make a fairly tough deck to beat, if you combine them with other cards of the same variety that you've come across in your travels. There's also a quasi-cardshark named Furko here who'll offer to play you a few times, with escalating wagers and more difficult side decks as you progress. Unfortunately, once you take him the third time, for 500 credits, he'll refuse to play for money after that. Still, you can clean him out of 750 credits altogether, if you have a decent deck.
Head down to the droid shop to inquire about this mystery droid that can speak Tuskan. Yuka will refuse to let him go for less than 4,000 credits, so exit out of the conversation afterwards and speak to HK-47, the droid in question. Go back to Yuka and you can knock the price down further with a persuade or Force persuade. Once you have bought HK, unequip one of your party members and add the droid to your party.
Before you leave the city, speak to Iziz the Jawa at the city gates to pick up the Fair Trade sidequest, which dovetails into the Sand People quest.