The Georgian House Hotel has been providing both beds and breakfasts to the weary traveller since 1851, and is a clean, well presented B&B. The staff were all very helpful, though I couldn't help but wonder if they wondered why a 32-year-old man was here to stay in a Harry Potter room by himself. Maybe this is a common occurrence.
There are currently four Wizard Chambers of varying size and appointment, though all are doubles. The room I stayed in, 43, is the only one on ground level; the rest are in the basement (the same night I stayed, my BuzzFeed colleague Chelsey and her husband were in one of the basement rooms, getting up to all kinds of mischief). With understandably high demand, there is a wait time of several months to stay in one.