Like garyjp says, it's gonna depend on a lot of things. Price to start out even a small zoo will really vary.
How big would it be? Where is it? You need a good location if you want to get enough visitors, but land is more expensive in urban areas. Zoning laws will need to allow for a zoo. Assuming you live in the US, different states will have different regulations relating to animals and you might need to spend more money on permits and such.
What kinds of animals would you have? Some animals will cost more to buy and maintain. Food costs can be pretty high, especially if you have large carnivores.
What is the staff situation like? Certain species would require specialized, experienced handlers.
You'll have to figure out vet care, again, costs for that can vary. I don't think small zoos usually have on-site vets. (feel free to correct me if I'm wrong) If there aren't exotic animal vets in your area, you might have to spend more to get them treated since the vet will have to travel far to reach you.
In addition to exhibits, you might need other facilities, maintenance and utility costs and such. You'll need a place to store and prepare the food, at least, and a way to shelter the animals if the weather gets bad. If the land you buy already has a building, that could possibly save you some money. Pay for water and electricity, along with insurance. You'll also want to have money set aside for emergencies.
Those are the bigger costs. Running a zoo would also have lots of small costs, again, that can vary depending on what you have. You'll have to pay for signage, trash cans, maintaining restrooms, advertising, souvenirs, vending machines, etc.
Starting a small zoo will probably cost you tens of thousands of dollars, at the least. Maintaining will also cost at least tens of thousands a year. You're not gonna be able to get a more exact budget until you figure out the details. Your biggest starting costs are going to be buying the land and building the facilities.