In July and August Europeans hit the road for their annual vacations.  When travelling in those months, reservations are a 'must'.  In June, however, most Europeans are still at work, the Gasthausen will be largely unoccupied, and you can always find a room for the night by inquiring at the local tourist information bureau.  Reservations are redundant and counter-productive.
What this means in a practical sense is that you can adjust your travel schedule as it suits you.  Are you bored with this town?  Move on; you can always find a room where you're going.  Is this place too charming to leave?  Stay an extra day or two; you don't have reservations that require you to be in a certain place on a certain day.
At the tourist bureau friendly volunteers will call around to the various B&Bs to find you accomodations at rock-bottom prices.  For a pittance you will get a clean, comfortable room and a belly-buster breakfast.  It almost doesn't matter where you stay.  This is the Gasthof goldener Greifen, boyhood home of Heinrich Topfer, Rothenburg's most beloved Mayor.  We stayed at the Gasthaus Kreuzerhof.
Rothenburg is a shopper's paradise.  Even Rick Steves suggests that you defer your souvenir purchasing until you get to Rothenburg.  The shopkeepers all speak English, in some cases better than the American tourists that clog their shops.  They are anxious to do business with you and, with just a little care and comparison shopping, you will get good value from them.