I'd really like to know, since as far as prepared hot dogs my part of NH (Dartmouth/Lake Sunapee) is mostly a wasteland (it's not bad if I'm making my own, I can get Deutschmacher and McKenzie's in the store easily enough, and I have a reasonable stash of Hummels in the freezer). Sadly, I mostly just grab steamed McKenzie dogs from some of the local general stores.
If I'm missing a good place, I'd really like to know. I'm seriously craving a good dog like a Blackie's dog or a Rutt's Hut ripper.
Better places I've found are:
Fabulous 50's in Newport. A decent selection of hot dogs and chili dogs, nicely cooked and toasted. They even have a Carolina slaw dog. Don't get the footlong, since they don't have proper footlong buns, so there's a lot of overhang (slaw dog pic at http://www.flickr.com/photos/kaszeta/169226749/)
For your decent-but-nothing-special Nathan's hot dog (with decent toppings options like kraut and chili), Scoop City in Claremont isn't bad (pic at http://www.flickr.com/photos/kaszeta/...)
And the hot dog cart in Hanover is good, but pricey.