how do cities influence weather in and around them?

Answer 1

Cities are enormous heat sinks. All that concrete soaks up heat and radiates it back into the atmosphere when the sun goes down. Cities are always hotter than the surrounding countryside.
Cities are also great producers of air pollution from vehicle emissions, factories, energy production, etc. CO2 and other elements (such as sulphur) combine with hydrogen, oxygen and other "natural" gasses in the atmosphere to create acid rain.
Some buildings are so large that they actually create microclimates within the city. Think of tall buildings that take up entire blocks - they act like man-made mountains and influence wind patterns and probably even precipitation.

Answer 2

The one most significant way I am aware of that they influence weather is that they cause the temperature to be higher. A city's structures give off great amounts of heat, as does car exhaust and the presence of humans in general.

The second thought is that high pollution might affect the air clarity, but that probably wouldn't prevent much heat from getting in. I am not aware of anything that would strongly affect precipitation amounts.

Answer 3

I don't think that they do.....