How can I tell boss im going to an eating disorder clinic?

Not full disclosure. You are likely under no obligation to reveal personal medical history to your boss, especially information you view as sensitive. It is appropriate to indicate that you have a medical appointment, particularly if a treatment plan may require frequent or scheduled work absences. Discuss with your boss how the family medical leave act (fmla) may provide you support in this circumstance.
It depends. While i agree with dr catano that you are under no obligation to share information about your health, just substitute the word "my cancer" for "my eating disorder" and act accordingly. It's time we stopped feeding into the stigma.