Coop - addresses. Just put in where you think you might be living into the text box on this link.
http://standorte.coop.ch/vstinfo/showMap.do?language=de
Alternatively go to the Swiss google google.ch and type in Coop. Then the map will come up with the nearest locations (did on my version, presume it will for you). Presume it will work for Migros too.
I love living in Luzern, I have also lived in Zurich and was also happy there. I wouldn't say that Zurich was anything like NYC from my visits to there, but I guess that is all personal opinion. You can always live just a little further out along the lake, this has another feel to it as well, maybe less like NYC for your wife.
My girlfriend commutes towards Basel from Luzern everyday and I agree the commute via car isn't the nicest. If you were in Horw, I guess the commute by public transport would be at least over an hour door to door to Zurich and Basel (more like 1.5 hours) which I wouldn't be interested in doing.
Like others I would be suggesting another place to live than Luzern from the information you have provided (such as Baden, Zurich or Basel which I know said you were against). Happy parents will help to have happy children (and if you are spending less time commuting that has got to help surely). But I can understand you wanting to base your move around your children, just not sure I could see it all working out.
Good luck with the move.