4 days on Milford
Spend night at Milford Sound (Or back at Te Anau but Milford sound is closer to the Routeburn)
Transfer to Routeburn Track. (Depending on transfer company you might be in luck and they could drop your next 5 days supplies after Milford Track at the Milford Accomodation if you stay down there, Kiwi's are pretty good with that kind of thing, even if a modest fee is involved)
Then walk the Routeburn and the Caples or Greenstone Track ?? (Transfer between Routeburn Shelter and Greenstone trail head)
Depends where your next stop is or if you are just there on a walking holiday.
Highly recommend the Routeburn. It's a lot more alpine than the Milford (for the most part)
When are you going ?? We were there in the first week in Nov 2011 and the Routeburn was closed still between McKenzie and Falls hut due to avalanche danger. Distance to far for the choppa to be economical, they bombed it open the day we walked out

and then commenced short flights over Harris Saddle in the danger zone (Wasn't that an interesting experience in the alps with explosives resounding off the Holyford Valley)
Or you could just do the Routeburn and a day walk or 3 around Queenstown. Ben Lomond which is straight above town is a great walk.
Planning another venture over there next March / April with the family. Can't get enough of the place, trip 5 for me.