There is no such thing as cheap education in the US. Academically strong students might be successful in finding assistantships that give them a free ride. However, comparable universities may have varying tuition rates. Generally, it is cheaper in the south (Texas, Louisiana, Arkansas, Florida, Georgia, Alabama, and Mississippi etc) than any other part of the country. This is usually one of the factors for students to determine where they would like to study.
Students can apply to as many universities as they choose. There is no limit on how many they would like to apply. They have to pay attention to the requirements and most importantly, deadlines while applying. Each university and the department within the university that is offering the degree program may have individual deadlines. Students should meet both the deadlines. And then there are financial assistance deadlines. Students who apply before this deadline will be considered for financial aid. These deadlines are earlier than regular deadlines. Sending your complete application sometimes can be very beneficial. Some committees evaluate applications as they come and others, wait till a certain time before they evaluate them in a lump. A student might get accepted if they apply early, particularly, if he/his is a borderline applicant.