If the law in NH works the way the law in CA does, a lawyer can appear for you on these misdemeanor charges. You would have to seek the advice of a NH attorney to know for sure. Also since an accident was involved, particularly if there were personal injuries, you may be facing felony charges in NH. You need to hook up with a lawyer quick.
This is an issue and unfortunately it may not take just a simple phone call to resolve this situation. I would first attempt to contact the prosecutor in New Hampshire and present the evidence that you have showing you were in San Francisco and the fact that you could not have been involved in the accident. This probably will not be easy or resolve the situation and you will most likely have to hire an attorney in New Hampshire to present this evidence to get your name cleared. I would repost this in the New Hampshire section and perhaps you can find an attorney that is willing to assist you for a nominal fee. Hiring an attorney will most likely be cheaper and more effective than you flying to New Hampshire and trying to resolve this on your own (assuming that the prosecutor will not resolve this over the phone and fax).
You really need to discuss the case with a lawyer in New Hampshire. If NH has a similar law to CA, a lawyer can appear 977 in your absence on a misdemeanor. However, a NH lawyer will be able to tell you if this is true in NH. If you are being charged with a felony, you will probably have to show up. However, a judge in CA can let an attorney appear in the client's absence on felony matters if the judge agrees and a form is filed with the court. See if a NH lawyer can confirm whether this can happen. If you can give a NH lawyer the evidence that you were in San Fran on the date of the alleged incident, it shouldn't be difficult to achieve. Call a NH lawyer as soon as possible. If there's solid evidence that you wern't in NH for the alleged DUI, a lawyer shouldn't charge that much to handle the matter.