So my favorite grocery store in Kiev and in Odessa has been Achaun. It's like a mini-SuperWal-mart. However...I did visit Santim on the recommendation of kkmail and like it as well. Many American brands. However, I now have a new favorite...Le Silpo. Not to be confused with Silpo (??????). It is a high end grocery store, much smaller than Auchan, but it is on the par of a normal grocery store in the U.S. Produce that looks nice (like it's supposed and not straight out of the babushka's garden). And a lot of American brands. They even have beef from Arkansas-based Creekstone Farms. They are the ones that supply beef to Boston Market, Friendly's, Johnny Rocket's, and Hickory Farms.
