We take our dog up to the north shore all the time, and he absolutely loves it. Honestly wish we would have taken him sooner (his first trip was at age 12-13). The only place that we ran into issues was at the lighthouse (Splitrock). No dogs allowed anywhere past the main entrance, though down by the actual pier was fine. Other then that, we haven't run into any issues anywhere between Two Harbors to Grand Marais.
Check out Black Beach if you've got some time - nice little gem of a place, won't take more than 30 minutes out of your day
