How bad would a drug use suspension effect my college applications?
No one but the admissions department at whichever universities could tell you specifically how it would impact your application—it almost certainly depends on the severity of the situation, and could definitely negatively affect your application process. Talk to your college counselor if you have one. Colleges don’t really expect students to be perfect, but do expect demonstrated growth. Some colleges have parts of their application which ask about disciplinary history and give you a space to elaborate on what happened.
If you are really concerned you can always do a community college for the first two years and transfer into a better university!