I try to avoid open strings. If I do use them, I use them either as an incomplete scale (eg Emaj scale starting on open E, forget about notes I don't have) or make sure the scale ends there (eg Em scale starting on open E). Or if I'm lucky I know that the scale I'm in has an E, A, D or G and I can use an open string. I do a couple of slides all across the fretboard (going 0->12th fret) to please the crowd a bit

Thus, you could use the open strings to 'move' into a more convenient note higher on the neck.
As far as 'what notes go with what', I'm not sure what you are talking about
