As a bar owner/operator, I feel that the responsibility of the cigarette butts is on the owner of the establishment and the smoker. If you (bar owner or manager) have the night door person, bartender or server sweep the Butts and empty the ash trays at the end of the night, you can usually be in good shape until later in the evening.
I don’t feel like it is the responsibility of the City to clean up after the people and the businesses. Maybe we can all pitch in and buy those businesses a broom to clean up after their selves. Technically, it is the responsibility for the smoker to dispose of their cigarette butt, it is garbage and if not disposed of properly it is littering. If this happens on your property it is your responsibility to clean it up, if you are unable to make the commitment you should not allow smoking on your premises, if it happens in front of your neighbor and you know that it is your guests, you should clean it up.

I appreciate GeneralStads bringing up the littering aspect. Too many times I'll be driving along and see someone throw their cigarette out the window. My car has even been hit by one before. Some smokers need to stop using the rest of the world as an ashtray.