Each character has their own individual safehouse. Every safehouse gives the player the opportunity to save the game by sleeping on the bed, heal with a First Aid Kit, change their clothing at a wardrobe, store vehicles in a garage, and watch the in-game television. The player is also able to use drugs (Jimmy's bong in Michael's House, Franklin's bong at the Whispymound Drive property and Trevor's gas in his trailer) and/or drink alcohol as well (Trevor's trailer). Weapons cannot be equipped inside and the beds cannot be used to save by other characters. For example, Franklin cannot save the game in Michael's House, and so on.
Despite a gameplay video showing the ability to search for a safehouse and purchase or go and check it out, this isn't available in the game. The website for searching safehouses claim its under maintenance, possibly for the release of Grand Theft Auto Online.