Okay, I'm no expert, but let me give you my thoughts.
I would guess that if you camped most of the time, about $30 per person per day might be about right. If you motel most of the time, you might be looking at about $50 per person per day (double-occupancy). As you say, a lot depends on your taste in food (and drinks and treats), accommodations and entertainment. The budget allows a bit for bike repair and supplies as needed. Let's see what others think.
You should be able to FedEx your bike either to a bike shop or to the motel you're planning to stay at on arrival or to a warm showers host. If you FedEx it to a bike shop, they could put it together for you (for a fee)--that might be good or bad. You can take whatever public transportation is available (bus, taxi, shuttle, etc.) to get from the airport to where your bike is. You can then ride from there to where you want to dip your wheel.