Tips for Fallout 1

I have just started Fallout 1, I went Shady Sands, and Vault 15, (I only got to the Vault entrance area, I killed a bear but I worried the rats would nibbled me down so I ran away). I also learned about the Rad Scropion issue. My biggest question is how exactly does the map/travel system work. I know it takes me places and stops if you encounter a creature or raider. Can you also just wander around with out the map thing? Like just exit the town area and wander the wastes? Other than that I do enjoy the game. I do love the challenge of it all compared to Fallout 3. I mean rats of all things are my biggest danger at level 1 lol.