The answer: Passport Health.
Passport Health is a clinic that specializes in travel vaccinations and immunizations and they have offices throughout the U.S. They'll tell you what you need and administer it right there in the office. They can also provide antibiotics (in case of a stomach bug), malaria pills and altitude medication.
Your regular doctor or pediatrician will likely not have most of what you need because their volume isn't high enough to stock the meds. That said, take your kids records with you so you don't duplicate anything they already have.