One of the first place to check would be, of course, the AMS website.
http://ams.org/programs/students/gradinfo/gradinfo
which also links to
http://orion.math.iastate.edu/dept/GraduateOpportunities.html
Though you need to be a bit more precise about what you mean by opportunity. Do you mean summer school? Internships? Teaching fellowships? Mentoring opportunities (where you teach some summer courses for undergraduates or advanced high-schoolers)?
And... if you are a graduate student, shouldn't you be either studying for exams or doing research for your dissertation?
