Congratulations @Rudy Planter on getting a house under contract! That's no small feat in this market, and your experience of multiple offers on multiple houses is pretty common right now, so kudos to you for your perseverance!
As you may know, New Hampshire is big on "local control," so the counties don't have too much influence, unlike other states. Any ordinances for or against STRs will be at the town level. Most towns make their Zoning Ordinances available online, so a Google search like "Wolfeboro Zoning Ordinance" will usually pull them up. If they're not online, you can find the town offices online and there's usually an email address for someone who can send it to you. Since regulation of STRs is fairly new and evolving, it might also be worth checking the minutes of recent Planning Board meetings to see if there has been any discussion on the subject, although it's probably easier to just ask whoever the Planning Board commissioner directly about that.
If you are considering condos for STRs, you'll need to look through the Declaration of Condominium, Bylaws, and Rules & Regulations for any prohibitions against rentals and for any minimum lease terms. If you need help with that let me know. Although some condo documents are readily available, sometimes they can be difficult to access them unless you're a unit owner, and some are behind paywalls; but often agents who are selling a unit will post them in the MLS, so I can go back and find them. If there are no restrictions in the condo documents, you'd be wise to do some further due diligence and make sure there haven't been any recent amendments that prohibit STRs, but at least that first sweep of the condo docs will show you if they've already been prohibited.
Ditto if a single-family home is in any kind of subdivision. There may be old covenants or HOA rules that haven't been enforced in years, but could be if an irate neighbor decided to pursue it. Usually those covenants will be noted on the deed, but you might have to go back a few deeds to get a book and page reference for them if they're a separate document and not explicitly enumerated in the deed itself. They're not likely to say anything about STRs, since those are a recent phenomenon, but they might say something vague about rentals, and vagueness is the attorney's playground
Following your guidance, I found zoning for Alton. Looks like "lodging house or and
