The strength of gravitational pull of the earth varies with height (more specifically distance from the center of the earth). It is maximum at sea level and decreases slightly both upwards and downwards. So an object would weigh more at a beach than on a mountain or under ground.
So if you knew what an object weighed at the beach and at the point of measurement, you can use the difference in weights and some simple math to get the difference in elevation between the beach and the the city.
Note : The decrease in gravitational pull is very slight and not noticeable. It requires precise instruments to measure but the logic is similar.
I believe it is also possible to estimate elevation based on other factors like air pressure which is also maximum at sea level and decreases as you go higher and higher.
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