I don't know any specifically for physics but there are many research programs you can participate (you can find many with a google search). You must apply to attend them typically and they tend to be very selective so you and your friend might be separated. The title specifies physics programs, but there are many research programs for math (e.g. The Ross program, PROMYS, Honors summer math camp, mathcamp).
I know this is pretty late to reply to this, but my son is also interested in summer physics programs, and I have found 2 so far that look pretty good.
One is at the Michegan State University affiliated with the National Cylcatron Unit (excuse my spelling). The web site is http://www.nscl.msu.edu/teachersstudents/programs [Broken]
on the left side you should see the option for "PAN"
This 1-week program is free, but you are responsible for transportation and room and board if necessary. They use the college dorms and have a cafetaria plan. Applications are due by the end of April.
Another is the California Sumer School for Science and Math taught at the UC campuses at Irvine, Santa Cruz, Los Angeles and San Diego. These are 4-week residential programs and cost about $2500 with everything included. Applications actually closed for these already, but you might want to think about it for next year. The website for these is http://www.ucop.edu/cosmos/
I just wish I had some of these options when I was in high school. I will be continuing to look into this, so just post again if you are still interested.
Beloit College in Wisconsin has a physics of music class this summer for high school students who will be juniors and seniors in Fall 2011. It is called Waves & Oscillations: Sounds & Science and is taught by the Chair of Beloit's Physics department, Paul Stanley. You can learn more about the physics class on our Summer LABS page: http://www.beloit.edu/summerlabs".