Cheap tickets to Europe

[bpc009]

Your cheapest alternative might be what ChromePony suggested:
SF - LON roundtrip, plus two seperate tix, LON-VIE and LON-STO

but I think it is better if you buy one round trip ticket from SF to either Vienna or Sthlm, and then purchase a separate round trip ticket VIE-STO or vice versa.

Unfortunately you don't have the best low cost air connections between STO and VIE. Air Berlin does connect them with a stopover in Germany, but alternatively SAS and Lufthansa both have started offering fairly cheap tickets in an attempt to compete with the low cost airfares. The prices are reasonable, I flew STO-VIE-STO in Sept for $175, and have the same trip booked a couple months from now for about the same price. You can expect to get the roundtrip fare for about $150 - $200 including taxes.