The town's hotel, inn, and apartment listings are in this downloadable brochure in both German and English:
By no means should you book the very dumpy Haus Menzel. I often book blindly in Germany with good results. Haus Menzel is the only place I've found that is grossly below standard.
The Hotel Goldener Kochlöffel has a great location in an adorable building right in town and close to the docks. I earmarked it as a place I'd like to try next time I'm in town. Rooms upstairs, restaurant down. I can tell you nothing else about it. You might investigate the place online:
The NH Rheinhotel Bingen is right on the river and not far from the docks. It rates "very good" and I see rooms for about US$80 on the dates I checked at www.hotelscomined.com