Public education in the U.S. typically lasts 12 years, (approximate) age 6 (first grade) through age 17 (twelfth grade). Most school districts also have an optional "kindergarten" for five-year-olds that most students attend.
After 12th grade, students continuing their education can go directly to university for their bachelor's degree (which is four years in the U.S.).
There is an intermediate degree: an associate's degree at a "community college" (public) or "junior college" (private). Some associate's degrees are vocational in nature (paralegal, dental hygiene, nursing, etc.); others are "transfer" degrees that can substitute for the first two years of a bachelor's degree.
Again, going to a community college for an associate's degree is -not- required; most students go directly from twelfth grade to university. Community colleges are open admission, so people who did not get admitted to university tend to go there; they also are usually inexpensive, so many people go there to save money on their education.
Most community colleges do not have dormitories; they are "commuter schools" where you would live at home with your parents while attending school. A few do have dormitories, though, and some have special housing programs for international students.
Private junior colleges typically have dorms, but they tend to be -very- expensive, even compared to universities (often "finishing schools" or "equine studies" for young ladies).