Talking about Postgresql, first of all you need to get a data of US cities boundaries shape file. Possible sites are
After that import data into postgres. I am assuming that your properties data is already stored in postgres. Make sure the SRID geometry type of cities boundaries is 4326. if not, you can convert it easily with ST_transform function.
Finally, to check which city some specific lat/long falls in, you need to convert the lat/long into point geometry and check against the cities data. e.g it would be some thing like this
SELECT c.city_name FROM cities_boundaries AS c, properties AS p
WHERE ST_CONTAINS(c.geom, ST_SetSRID(ST_MakePoint(p.longitude, p.latitude), 4326))