Find timestamp for highest number of concurrent users by date

Just apply the DATE() function in the aggregation of concurrent_timestamp

select
    DATE(concurrent_timestamp) timestamp_date
   ,max(concurrent_users) max_concurrent_users
from sample_data
group by DATE(concurrent_timestamp);

In PostgreSQL you can simply use DISTINCT ON:

SELECT DISTINCT ON (concurrent_date) *
FROM   sample_data
ORDER  BY concurrent_date, concurrent_users DESC;

We don't need the redundant column concurrent_date for this at all. Casting concurrent_timestamp on the fly is very cheap - overall cheaper than storing the functionally dependent value redundantly.

SELECT DISTINCT ON (concurrent_timestamp::date) *
FROM   sample_data
ORDER  BY concurrent_timestamp::date, concurrent_users DESC;

db<>fiddle here

See:

• Select first row in each GROUP BY group?

DISTINCT ON is typically fastest for few rows per group. Depending on table definition and data distribution, there may be (much) faster solutions. See:

• Optimize GROUP BY query to retrieve latest row per user

You can do something like this in mysql

CREATE TABLE sample_data (
  `concurrent_users` INTEGER,
  `concurrent_timestamp` VARCHAR(30),
  `concurrent_date` DATE
);

INSERT INTO sample_data
  (`concurrent_users`, `concurrent_timestamp`, `concurrent_date`)
VALUES
  ('3', '2020-06-24 07:20:00 UTC', '2020-06-24'),
  ('7', '2020-06-24 08:20:00 UTC', '2020-06-24'),
  ('8', '2020-07-05 06:20:00 UTC', '2020-07-05'),
  ('2', '2020-07-05 03:20:00 UTC', '2020-07-05');

select concurrent_timestamp, maxid 
from sample_data s INNER JOIN (select concurrent_date, max(concurrent_users) maxid
from sample_data
group by concurrent_date) s1 ON s.concurrent_users = s1.maxid; 

concurrent_timestamp    | maxid
:---------------------- | ----:
2020-06-24 08:20:00 UTC |     7
2020-07-05 06:20:00 UTC |     8

db<>fiddle here

This is a "groupwise-max" problem. You can't do it with a simple query, you need a subquery. There are many examples off the tag I added. Or you can read my blog: http://mysql.rjweb.org/doc.php/groupwise_max