It is known that for every 100 meters of terrain elevation, the atmospheric pressure decreases by 0.6 degrees Celsius. Accordingly, if the city has an excess of terrain, then in different parts of its high-altitude climatic conditions will be different. If the settlement is located in a closed basin, then its climatic conditions will also be different in comparison with the environment.
, the question is about climate change within the city. I agree that you are right if the city is located on the slopes of mountain ranges with large terrain excesses.
Depends on the City! Here in the San Francisco Bay Area, which is one big 7 million person "city"-- you go a few kilometers in any direction and the daytime temps can change in the summer by 30 degrees F.,
And the nights in winter can change by 15 deg. F. and the wind speed from the lowlands to the top of the 3,000 foot (1,000 meter) peaks surrounding the city area can go from 10 mph to 60 mph during the same night.
Also, annual rainfall can change even more radically, going west to east in 5 kilometer jumps: 20 inches, 80 inches, 12 inches, 30 inches, 8 inches.
You should let us know what city you are studying, so we can give you specific answers?
Other changes you should expect depend on the amount of reflective surfaces (roofs of buildings may reflect the sun, asphalt on roads absorb the sun's energy) and amount of green space (green absorbs sun's energy).
I think so broadly speaking due the general climate becuase higher elevation will certainly have lower general climate and vice-versa. The micro-climate within the the city may vary based on numbers vehicles and human population. Best regards.