The New Hampshire Supreme Court has held that a party effectively consented to the recording of a communication when the surrounding circumstances demonstrated that the party knew the communication was being recorded. New Hampshire v. Locke, 761 A.2d 376 (N.H. 1999); see also Fischer v. Hooper, 732 A.2d 396 (N.H. 1999) (upholding the sufficiency of an instruction that the jury could consider, under the standard for implied consent, not only a defendant’s words but also her actions in determining whether she consented to the recording of her conversation), superseded by statute on other grounds. More recently, the state high court ruled that a criminal defendant consented to the recording of a real-time online conversation because he knew that the recording on the other party’s computer of the instant message was necessary for its recipient to read the communication. New Hampshire v. Lott, 879 A.2d 1167 (N.H. 2005).
More pertinently (from the same link):
In-person conversations: It is unlawful to record “any verbal communication uttered by a person who has a reasonable expectation that the communication is not subject to interception, under circumstances justifying such expectation” without first obtaining the consent of all parties engaged in the conversation. N.H. Rev. Stat. Ann. § 570-A:1. Thus, a journalist does not need consent to record conversations in public where there is no reasonable expectation of privacy.
The law, however, does not criminalize the use of recording devices for other purposes in areas in which there is no reasonable expectation of privacy (i.e., filming conversations on public streets or a hotel lobby). The state Supreme Court found that a classroom was not a private place where a school custodian could reasonably expect to be safe from video surveillance. New Hampshire v. McLellan, 744 A.2d 611 (N.H. 1999).
So, no, it does not seem that NH is among the few states which criminalize the recording of conversations in public places.