Planning on making a Way of Shadow Monk & saw something about the spells that I noticed.

You get Minor Illusion as a cantrip but how do you calculate the spell save DC for when someone is investigating it?

From the Ki feature of Monks:

Some of your ki features require your target to make a saving throw to resist the feature's effects. The saving throw DC is calculated as follows:

Ki save DC = 8 + your proficiency bonus + your Wisdom modifier

Even though it's a cantrip and doesn't use Ki, use your Ki save DC.

Monks base their saving throws on their Wisdom score. So 8 + their proficiency modifier + their Wisdom modifier. 

Thanks everyone for the replies.