Although this question has been answered, here are some more details.
Read this article: Aliens and Non-U.S. Citizens Seeking Flight Training
UK participates in Visa Waiver Program. So you do not need visa for 90 days.
However, I could not find any information if you need visa for flight training or not. TSA does mention that a visa is required (see this: Alien Flight Student Program), but they did not specify which visa type.
After more research, I found that you need either an F-1 or M-1 visa. It is also mentioned in magazine Flying.
Where can a foreigner lives depends on how much money the foreigner has. We Americans respect and honor a rich foreigner the same way as a rich American. No discrimination.
Living expenses greatly varies where you are living. ATP Flight School provide housing for students, but they have a 6-month program from beginning to all the way to an airline pilot. You can contact them to inquire if they can just teach PPL. You can search for smaller flying schools to find out about the housing options they provide or have nearby.