Have a good read on spatial relation functions in PostGIS, and get aquainted with the detailed usage parameters of those functions via the PostGIS docs. I dare say this is the most frequently used functionality in spatial database analysis; as a beginner (I hope I assume correctly) and for simple tasks, knowing about those alone will drastically improve your work with PostGIS.
In this basic case, ST_Intesects will most likely be the one you are looking for:
WHERE ST_Intersects(geom, 'POINT(71.013 11)')
This should return all city names in
<city_name_column> that spatially intersect with the given point.
However, this already implies knowledge about a few other things, e.g. the coordinate referrence system you are using. For all relation functions to make sense, the geometries to be compared must be referred in the same CSR. If that is not the case, you will need to transform one of those CRS to match the other.
Sidenote: while the use of ST_Intersects is rather straight forward, other spatial relation functions do have specific behaviours and need to be used with care to get proper results (e.g. the order in which the geometries are given to the function, etc.). ST_Within(A, B) for example returns true if geometry A is completely inside geometry B (note the order), which, unlike ST_Intersects, does not consider a point if it lies on the boundary of a polygon.