Many universities, professional societies, and national research laboratories offer summer internships and/or research programs for undergraduate students from across the country. These typically offer a stipend and/or support for travel and living expenses to enable all students to afford to attend. Your research advisor at such a program will likely be a good source of advice about careers and graduate programs. Applications are usually due about 6 months in advance.

NASA Undergraduate Student Research Program

National Institute of Standards and Technology Summer Undergraduate Research Fellowships

National Institutes of Health student programs

National Science Foundation Research Opportunities for Undergraduates

Naval Research Laboratory student programs

US Dept. of Energy Summer Undergraduate Laboratory Internships

American Chemical Society

American Mathematical Society

American Physical Society

American Physiological Society

American Society for Biochemistry and Molecular Biology

Other off-campus opportunities