I find 400 to be a good speed for a dim cloudy day, or for shooting in indirect-daylight situations like under a tree canopy. In full sun it's often too fast, yeah.
Nighttime and indoors are such variable lighting situations that it's hard to generalize. I've done street shooting at night with an f/4 lens and a push to 800; if it had been an f/2.8 lens I could have been shooting at box speed. But those were some pretty well-lit streets, and there are plenty of situations where even 3200 isn't really fast enough for comfort.
Your suggestion---slower film in daylight, push in darkness---is basically what I do most of the time. I guess you could also carry a monopod to the bar (or brace your camera on a chair, pool cue, drunk, or whatever else is handy) or invest in seriously fast lenses. Or try putting together an infrared flash; I never got it to work to my satisfaction, but some people have had good results that way.