What are the best universities in which I can study graphic design or publicity?
A good art school will have a portfolio review as a requirement for entrance. That is a good metric of how serious a school it is. Any school without that type of admission standard has probably got a weak program. If money is no object and you are talented, try the Savannah College of Art and Design, Parsons, Ringling or Full Sail. As for the publicity component, any good state university that offers a major in advertising/public relations should suffice. Bottom line is that the school does not make the student, the student makes it for himself. Nothing will substitute for hard work. IMHO selecting an art school is a more critical than other types of degrees because when you enter the job market, your diploma will not mean nearly as much as the portfolio you have to show. Better schools and better professors will challenge you more and are more likely to give you the kind of feedback you can use to improve your portfolio. Best of luck!