In addition to your starting house on Grove Street, you are able to purchase additional safehouses in the world. There are six you can purchase in Los Santos alone, although one or two might be a bit too expensive for your taste at that point in the game. The other four, though, cost $10,000 each, which is perfectly reasonable, especially once you unlock the Gang Warfare and can earn a little bit of money before the end of the Los Santos missions. Safehouses you can purchase are shown as a little green house icon on your map. There are more safehouses later and while they might be a little more expensive, you should have more money by then, too.