SQL - Min Function...

SELECT *
FROM (
    SELECT venuename, 
           costperday,
           min(costperday) over () as min_cost,
    FROM venues
    WHERE venuecapacity = 120
) v
WHERE v.min_cost = v.costperday

Or using a subselect:

SELECT *
FROM venues
WHERE venuecapacity = 120
AND costperday = (SELECT min(v2.costperday) 
                  FROM venues v2
                  WHERE v2.venuecapacity = 120)

You might want to use venuecapacity >= 120 in case there are venues that accomodate more than 120 people but are still cheaper than others that only allow exactly 120 people

select v.venuename, min(v.costperday)
from 
(
  select venuename, costperday
  from venues
  where v.venuecapacity = 120) v

That is because you select the lowest cost per day per venue if you include the name. In fact, the whole grouping is useless in this table as long as venuename is unique.

To get the venue with the lowest price use something like this:

select venuename, costperday
from
  venues v
where
  v.venuecapacity = 120 and
  v.costperday = (select min(costperday) from venue vs where va.venuecapacity = 120)

I think this might be what you want:

SELECT venuename
  FROM (SELECT venuename, costperday, MIN(costperday) OVER () mincost
          FROM venues
         WHERE venuecapacity >= 120) q
 WHERE q.costperday = v.mincost;

Use >= 120, because you might not have any venues that have exactly 120 capacity, and you want all venues that can handle at least 120. Your requirements only state that the venue be able to accommodate 120 people, not that it handle exactly 120 people.

You include the same field in the select list, thus the min will be computed for each of them not overall items