Yup, it can all be done in one place. In fact, under the rules, anybody with the appropriate flight instructor ratings and access to an airplane could do the training for you, but if you don't have the appropriate documents (such as US citizenship or green card or appropriate visa), you would have to go through a school approved to get you a visa for training. But most schools in the US would be able to get you where you needed in a relatively short amount of time, depending on personal ability.
There are also hundreds of testing facilities around the US where you can do your knowledge tests (theory tests). Many of them are actually located at the schools.
CATS Testing - Site Search
PSI Online - FAA Exams
Just have a look...