I did some poking around in the documentation for Calculated field formulas, but I don't see anything that would help me do this. Does anyone know if it can be done? Can you point me in the right direction?
In the Default option you can use [Today] plus some number of days... you would have to find the weekday as an integer, compare it to the weekday of Today as an integer, and do some math to get something to add to [Today] to make it next Friday. I'll see if i can find the right formula for it in the mean time.
Edit: ok so you can use WEEKDAY([Today]) to return an integer from 1 (sunday) to 7 (saturday) (Options of WEEKDAY Function), and depending on how you want to determine what 'next week' is, you would add write the formula as something like...
Haven't tested it but that should work!