I’m going to be a rising junior and I’m not very close with my current science or math teachers. I’ve only spoke with my high school counselor once for 5 minutes, so I’m not very close with him either. A lot of the programs I’ve been looking at require recommendations however. Are there any other great computer science programs out there (preferably in the northeast)?
You can look at mysummeradvisor.com for some ideas. You can search under Academic Programs, Technology. ID Tech does some great programs. In the past, they have held programs at Bentley, which is in the suburbs of Boston. University of Maryland has some Cyberdefense camps that look interesting.
For letters of recommendation, don’t worry that you aren’t close to your teachers. These programs want to make sure that you aren’t going to be a pain, because they are stuck with you for the summer. They also want to know that you are capable of doing the work. If you have gotten a good grade in a class, just ask the teacher. It is a way for them to get to know you. You will need letters of recommendation for college anyway, so you might as well start making some connections.
I don’t know if Rose-Hulman’s Operation Catapult requires one, check it out. Even if it does, as long as the teacher knows who you are from class and you got a good grade, it will probably be sufficient. 
They just don’t want to let in real jerks. Although Catapult is an engineering program, quite a few students do programming related projects every summer.