I will be in Schweinfurt for 4 days and need to find some day tours of surrounding areas.... Are there bus tours available from hotels in this area?
Not sure about bus tours, but via train you should be able to see Wurzburg, Heidelberg, and Rothenberg. TC
Are you staying with someone in the US military stationed there? Schweinfurt is not really a tourist destination, so I would doubt you would find any tour buses from there. I know the US base there is shutting down, but sometimes the USO sponsors outings.
If your visit has nothing to do with the US military, and you're not renting a car, go with the train.
The military bases in Bamberg and Schweinfurt will be closed this June-July, so I would not expect any services there (MWR, USO etc.). A train trip to Bamberg and/or Nuremberg and Erfurt are probably doable. All have great old town centers.
You can take trains to other towns. Look at a map on Google and find other interesting towns to visit that are close by.