Im trying to create a formula from one column where all of our members manually inputted their location (NYC, LA, SF) and input it to another column where I have them as multi select. So ideally any record that contains New York City will fall under NYC, Los Angelas will fall under LA.
Unfortunately this isn’t something you can do with a formula. Formula’s are a type of field, so the formula resides in its own field (column). The formula can affect what its own cell displays, but the formula cannot change the contents of another field.
What you are wanting to do sounds like something that will either have to be handled by:
Some form of manual transferring (for example, a formula field that converts the user input into text resembling your multi-select options, which you then copy-paste over into your multi-select field, or use a Batch Update Extension to copy over)