I usually just stick to a Diet Coke when I'm at a bar and not drinking. I would guess that is the #1 non-alcoholic drink ordered at bars. If I'm not in the mood for diet coke, I'll get a club soda or something. In general, I try to avoid situations in bars where others are binge drinking, though.
If you're a coffee addict, like I am, you'd be surprised how many bars have coffee as well.