It really depends on your situation.
Days to Avoid
The days to avoid are the days when there is the biggest demand for seats.
That’s when business travellers and leisure travellers are wanting the same flight
Typically Fridays are bad with people setting off for holidays at the same time as business people returning to their home base.
Sundays is similar with people returning from their holidays and weekly commuters returning to be ready to start on Monday morning.
When I worked full time I used to be be caught in this trap when travelling for leisure as I wanted to get the most use out of the limited leave available.
That meant including as much of the weekend in the holiday as possible.
Convenience was more important than cost!
Cheapest Days
Generally the cheapest days tend to be midweek, typically Tuesdays and Wednesdays.
Thursday and Saturdays are normally not too bad.
Now I am retired I like to take advantage of the midweek lower fares.
When we book cruises, or tours we now look to go a couple of days earlier and stop on a couple of days afterwards.
Not only do take advantage of lower fares, but if a flight is delayed we don’t risk missing the start of the cruise.
In this case cost can equal convenience!