I would try a couple of other places on the Rhein, if that is where you really want to go. There are several places in Bacharach. I would try Im Malerwinkel. Rick's books suggest some others.
You might try a place in Braubach, especially if you plan to see the Marksburg. I like Weinhaus Wieghardt.
Boppard (www.boppard.de) is lovely, with some major hotels lined up along a riverfront walk. One of them, the Bellevue, is a Best Western. You could book on their site.
As for Würzburg, I spent two nights there in Oct 07. I stayed at Pension Spehnkuch, which is listed in Rick's guidebooks. It's very inexpensive and only a block from the Bahnhof. It does have the bathroom down the hall, but I never had a problem with that. There is a streetcar from the Bahnhof to Marienberg, the fortress on the hill across the river. I really enjoyed Marienberg. From there you can take a bus to the Residenz; I didn't like it as much - too ornate. I walked back to Spehnkuch from the Residenz.
I spent part of a day (mid-morning to mid-afternnon) in Nürnberg, and felt I had seen everything I wanted to see.