How can the materials that cities are constructed of lead to the development of microclimates?
The difference in albedo and heat absorption of different materials greatly effect microclimates.
Microclimate can be an area as small as a few inches to as large as a few miles, where the climate is altered by local effects. The best example I can think of, especially for your question, is the city heat sink.
If you have ever walked across an asphalt parking lot in bare feet on a sunny warm day, you know that asphalt has a very low albedo (reflectiveness) and readily absorbs heat. A low albedo means that very little of the sunlight that hits it is reflected, so it is absorbed and that increases the temperature.
The albedo of green grass is about twice that of asphalt. If you have a city in a area of the world that would normally be grass, and that city has a lot of asphalt shingles and roads and parking lots, the city is going to absorb a lot more sunshine than the climate of the area would suggest, and therefore the city is going to be hotter. This is a micro climate.
I just want to add something, since many people that deny global warming use this point to suggest that man-made green house gases are not as bad as suggested. Most studies of climate change factor in the heat sink effect of cities. Some will argue that the factor is not enough. However this is a very flawed argument.
The official temperature of a city is measured at the airport. That means that it is in an area with a fair amount of open grass around, and that it is either on the edge of a city or the outskirts or in some cases a few miles from the city. This means that factoring in the heat sink effect is enough and in some cases more than enough.
The second problem with the argument is that heat is heat. If an icecap is melting does it make any difference if the heat is due to the heat sink effect of a city or to greenhouse gas emissions.