Traveling with 4 family members totaling 2 adults 2 teenagers.

Hi there! Flying from San Francisco to Tokyo for 5 days, Train to Kyoto for 3 days. Plan on heading to Seoul for 5 days and returning to SF from Seoul.

Should I take a flight from Kyoto/Osaka airport to Seoul or should I take the train back to Tokyo for a night, and then fly out to Seoul?

Osaka (KIX) to Seoul (ICN) has some cheap fares. Traveling back to a Tokyo airport c/would cost more than the flight.
Use these airport codes to search for fares using multiple airports in each city.
OSA = Osaka KIX and ITM
SEL = Seoul ICN and GMP
TYO = Tokyo HND and NRT

Youl will probably find that Osaka is best

But it should be possible to get an open jaw
SFO-TYO, KIX-ICN-SFO all on one ticket