How can I unlock the whole city on the PC version?

There is no cheat that unlocks the entire map. You could however:

• Explore the map with a plane, (enabling the "Lock Wanted Level" cheat to make the Cops not chase you).
• Use a Savegame from someone who has unlocked every area. This is probably the easiest method. It shouldn't be that hard to find a save on the Internet.
• Create a Savegame like you want it to be with a Savegame Editor. I haven't tested it myself, but you should be able to create one relatively easily using that.

Did you consider downloading a save-game that has all the missions complete? You will also find plenty of save-games with each mission complete here:

http://www.gtasavegames.com/savegames/San_Andreas

Since there is no character customization in this game, I would personally not mind downloading and playing, if it's just for nostalgia :)

I managed to edit a saved map with the GTA San Andreas Save Game Editor and change my "first safehouse" to different areas, and then go ahead buy a new one and then just change my first safehouse again and do so. This made me be able to own every house in the game, this was the result I was after. I just hoped for a faster and easier result. But thanks everyone! :)

I haven't got the final part of the map working. When I enter the monstertruck at one of my "girlfriends" workshop the game just crashes. So I guess there is a problem with my method on unlocking the whole map.

so the outline is It sort of works.