Otherwise I'd think your best bet is either Uptown or Lyn-Lake (if you want something other than just wine or beer). Heidi's has good cocktails; Il Gatto and Barbette also have good drinks. There's just not a lot of cocktail options in the more neighborhood-y areas, they usually only have a wine/beer license.
5411 Penn Avenue South, Minneapolis, MN 55419
3001 Hennepin Avenue South, Minneapolis, MN 55408