Wow. You're a college student, and so you have lots of skills. Why not use them during the summer? Better yet, why not do something that will also help you determine what you want to do later in life?
If you want to know what research is like, try doing research in a Research Experience for Undergraduates (REU) program. If you're thinking of graduate school, trying an REU is almost a must! They're lots of fun, and you get paid, too. Application deadlines are mainly in February and March. If you want to know more about whether an REU is right for you, check out this older article on the MAA website on Is an REU for you? and this newer summary What can an REU do for you?
REUs receive many many more applications than they have spots (they're more selective than elite colleges!), so it's a good idea to apply to at least 6 of them. They also vary widely in structure (for example, whether students work individually or in groups, on similar projects or different projects, with lots of faculty supervision/interaction or very little). If you've been accepted to more than one REU, be sure to ask about the details of the structure if these aspects of your working environment are important to you.
Many programs are restricted to those undergraduate students who will not have graduated before the program begins (that is, they exclude current seniors). The following five programs do accept applications from graduating seniors:
The Park City Mathematics Institute (PCMI) has an Undergraduate Summer School which interacts with the Graduate Summer School and Research in Mathematics programs. (Click on the Undergraduate Summer School link at the top of the page. They change the URLs regularly.)
NIST SURF is the National Institute of Standards and Technology's Summer Undergraduate Research Fellowship with projects in applied mathematics.
IPAM is the Institute for Pure and Applied Mathematics. It hosts the Research in Industrial Projects (RIPS) for undergraduates and recent graduates.
The National Security Agency has a variety of summer programs, some of which are research-based (such as the very-exclusive Director's Summer Program). They all have October 15th deadlines; be persistent in navigating the Intelligence Careers website, as there are few internal links to find information.
Just for Women:
The Institute for Advanced Study (IAS) hosts an 11-day workshop for Women and Mathematics each May.
About to go to graduate school? Consider the EDGE program for the summer before you start.
Just for non-U.S.citizens:
Very few U.S. summer programs have funding that can be allocated to students who are not U.S. citizens or permanent residents. Those that regularly have such funding include
the SMALL REU at Williams College
RIPS at the Institute for Pure and Applied Mathematics
PCMI will fund living costs for students from any country, though only U.S. citizens or permanent residents are eligible for stipends.
Some undergraduate institutions will provide funding for international students to do summer research or study at other institutions. Check to see whether you can obtain funding in this manner. If you can, or if you can otherwise finance travel and living expenses for the summer, then more summer mathematics programs will consider your application.
If you're interested in trying out the world of industry (business, actuarial, technology, etc.) you might look for an internship.
What if you want some teaching experience? Try looking at middle-school and high-school enrichment programs---many of them hire undergrads to assist with teaching or homework.