You do know that starting your RTW in ICN is considerable cheaper than it is in NYC. Using some miles to get there might save you money, and with a stopover in SFO you could even see your family on both directions :-).

Or look at buying some US Airways miles now the promo is running and make it a US-EU-ICN trip with a stopover (and maybe some additional low cost tickets to the other destinations). Your RTW includes only major airports so an RTW might not be the best deal, unless you need the flexibility it provides. Or even combine the two :-).