@Adam's answer is definitely more helpful. Although I think we can improve on it again because if we're truncating a Timestamp to a single day (or week/month/etc), then we want to make sure that we're dealing with a Date object, not a Timestamp. Otherwise we may give other pieces of code the impression that something just actually happened to occur at midnight (or potentially some other misleading time of day).
So I would use:
SELECT date_trunc('day', some_timestamp AT TIME ZONE users_timezone)::date AS the_date;
which casts the result to a Date, rather than Timestamp.
The result will be something like:
the_date
------------
2019-09-14
instead of the more misleading result of:
the_date
---------------------
2019-09-14 00:00:00