All University of California (UC) schools require Subject Tests - so no luck there; especially if your are an out-of-state resident.
Remember that Washington University in St. Louis is an extremely competitive school to get into so if your son is deficient in an area (GPA, SAT, EC's,...) it could benefit him if he took some SATII's.
Remember, your son could always take the SATII's by being a standby taker.
Some colleges also waive the SATII requirement if one submits the ACT (Yale, Upenn, Tufts,...)-- although, the UC system unfourtantely is one of the places that does not do that.