Want the Safari Zone without having to pay? Then you can go Area Exploring! The Pokémon you find via Area Exploring won't be a patch on the ones you can find via the Safari Zone, though you can catch Pokémon you may never have caught in the Safari Zone in the areas. You will have to buy Poké Balls, though you get one free if you have less than 5 Pokémon.
In exploring, you will have to fight with one of your own Pokémon, and only one. If your Pokémon is knocked out, that's it. If the enemy is knocked out before you catch it, that's it, no catching. Finally, if you encounter a Pokémon you don't want, you can simply say that you don't want it, though that counts as one of your area visits.
You can go to 3 areas per day, or visit one area three times, or visit one area twice and another once, etc. Abuse of area privileges may result in a ban from the Safari Zone and Areas Exploring.