To get no enemy encounters as you're walking down the streets, you need the Beads of Good Fortune. To get them you require 100 Completion Points.
Obtaining Beads of Good Fortune
1. Get to the bottom left of Kamuracho, as seen on the map.
2. Near the famous Kamuracho Gate look for a guy wearing clown makeup.
3. Ask to trade completion points.
4. Go to the section called BATTLE, spend 100 Completion Points until you reach 'Beads of Good Fortune'.
Congratulations! Now no enemy will try and attack you.