Trinity's Problem of the Week and Purdue's Problem of the Week were both weekly problems that were excellent for college math clubs to tangle with at their weekly meetings. However, both of them are no longer posting new problems.
What is a good replacement?
A good answer would involve contest-type questions but they would not be part of a contest. Or, if they are part of a contest, the competition part of it should be clearly de-emphasized. The point is to engage with interesting problems for the sake of themselves.