There are a number of excellent summer math programs for advanced highschool students. I have my own opinions of which are better or worse, but a quasi-objective list of the programs you'd want to consider can be found at the MIT list of "other selective math programs.
In addition to the usual AMC math competitions, there's USAMTS and ARML. USAMTS is nice because it's not done in an exam setting. ARML is in person and so lets you meet lots of other math people. There may be more good competitions that have cropped up since I was in highschool.
Some internet resources include AoPS and math.SE. I don't know a good list of all the good internet resources.
Any other advice is going to be highly location specific. For example, in Boston there's the new PRIMES program. One bit of generic location specific advice is to see if the nearest good college has any programs for advanced highschoolers, or even just ask around the nearest math dept.