At the start of the game, it seems like you can only save two cars parked in the "Residents Parking Only" parking spaces in front of your safe house. However, if you can find other "Residents Parking Only" places around the city, you can also save cars there even if you do not have a safe house at those locations yet.
Outside your first safehouse is a small parking area marked with "Residents Parking Only" signs to park vehicles and save them. Do not park your vehicles fully within the lines. Instead, park vehicles partially within those lines to have more vehicles parked and saved there.
This trick only works up until you leave the current game session. If you shut off your system and play a multiplayer game or load your most recent save, all but two of your cars will have disappeared. It seems to either save the two cars closest to the center of the parking space, or save two at random.