I shop at both Shop Rite in the City Center and Stop and Shop on Mamaroneck Avenue across from The Westchester Mall and the one in North White Plains for staples. Whereas Whole Foods is more expensive, I go there for fresh fish, meats and specialty items. Their fruits and vegetables too meet a higher standard in my opinion. Variety is the spice of life...try something different and go to the H Mart grocery store on Central Avenue in Hartsdale, bordering Battle Hill in White Plains. It's a new, fabulous Asian Grocery store that caters to all. Prices are good. If you are familiar with Fairway Markets...there is one in Pelham at 847 Pelham Parkway, it's suppose to have good prices as well. Of course there is always Stew Leonards in Yonkers of Route 87. It's an experience. I go mainly when I'm entertaining and want a great cut of Fillet Mignon, can't beat it.
I frequent my Super Stop & Shop in New Rochelle, and would have to mention Stop & Shop in White Plains - located at 154 Westchester Avenue. Many people (myself included) go to Whole Foods located at 110 Bloomingdale Road (8-10 p.m. 7 days a week) but not many great prices there - just a great selection of healthy, organic foods.
Apple Farm on Tarrytown Rd. is wonderful! It's a produce market, not a supermarket, but you cannot beat it for its freshness and its prices. (It also has fish, meat, and cheeses, but I am not as familiar with those offerings.)
The 2 major super markets carry the staples and have good variety as well as specialty food. In addition if you are looking for fresh produce, fish and meats, try Apple Farm at 37 Tarrytown Road and the new H-Mart at 371 N. Central Ave. It is on the Hartsdale/White Plains border.