There are all kinds of Research Experiences for Undergraduates (REUs) listed on the NSF website. These internship opportunities are at many different institutions throughout the USA.
"NSF funds a large number of research opportunities for undergraduate students through its REU Sites program. An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific research project, where he/she works closely with the faculty and other researchers. "
Note: Students must contact the individual site or program to apply. NSF does not have application materials and does not select student participants.