Here are some central neighborhoods to visit with the name of the subway stop in parentheses.
2. Patriarshy Prudi (Mayakovskaya, Tverskaya)
3. Tsvetnoy Boulevard (Tsvetnoy Boulevard or Trubnaya)
4. Hamovniki (Frunzenskaya, Park Kultury)
Supermarkets have a pretty clear hierarchy. It works like this. You have the extremely high priced chains- Globus Gourme and Azbuka Vkusa, which do provide quality imported foods for those willing to pay. Slightly lower priced and similar quality are Zeleny Perekrestok and the Tsvetnoy Central Market (one location- in neighborhood 3 above).
Perekrestok and Sedmoy Kontinent come in next for lower prices and pretty much acceptable standards but not for everything.
Then you have Dixy, Magnolia, and a couple others for discount prices for basic foodstuffs.
Many people shop at better priced bulk retailers like Auchan and Metro which are outside of the center but a bearable distance. We also have Ikea and Mega, all four of the above have several locations out of the center.
For stores, shopping in Moscow ranges from highly marked up designer imports at department stores TSUM and GUM, (very central, next to Bolshoi theater and on Red Sq., respectively) to discounted but still dubiously priced Podium Market at Moskva Mall (Torgoviy Dom Moskva) across from the Bolshoi at the back of the new Four Seasons hotel.
Moscow has a lot of cheap small independent retailers called “Produkty” for food and household goods; it is still better to shop at the bulk retailers.