"Open to opportunities" vs. "open for opportunities"

The first one is correct. "Open to something" means that you're willing to consider something; that you're agreeable to hear or learn about new ideas and suggestions. For example: "He's open to any reasonable suggestions." So, in your case, "I'm open to new opportunities", means that you're willing to consider any new opportunities. As for "open for", I agree with anongoodnurse.