I have a parrot size travel case that I use to take my parrots to the vet. Perhaps you could use something like it for going into stores and restaurants, etc. Much less noticeable.
http://www.amazon.com/Bird-Traveler-Case-Floral-Blue/dp/B000HI2KVW/ref=sr_1_1?s=pet-supplies&ie=UTF8&qid=1369677750&sr=1-1&keywords=travel+cases+for+birds
Also if you get some fast food, there are parks all over with picnic tables, restrooms and all. Fresh air and sunlight and yummy food.
As one of 7 kids in a family, I commend you for taking the trip. My Dad would make us count off before he left a place to return home so he wouldn't lose one or two. Great memories.