What are you looking for? Are you looking for just a couple of snacks and some drinks or a full grocery store?
As Elizabeth said, the closest store is Maho Market. I personally don't care for it very much, if you're looking for a full grocery store, but it will definitely do if you're just looking for a few things. Parking is tight, but doable. They are open on Sunday till perhaps 11 PM or so.
A bit further would be Carrefour Market, past the airport, across the causeway and turn right. A full, wonderful grocery store, good prices, nice produce, better parking than Maho, although still not great, and now open until 6 PM on Sundays.
Market Garden is in Simpson Bay, at the corner of Billy Folly Road, full grocery store, open till I think around 9 PM, ample parking, prices are higher than the others, but a full produce department.
My two favorites at the moment are both a bit further, Super U in Marigot, having a senior moment, but I think also open till 6 on Sunday, great prices, wonderful parking, on the French side in Marigot, but a quick trip now, over the Causeway. My other favorite is Grand Marche by the roundabout, the furthest in time, but again open until 6 PM now, good meats and produce, good liquor and wine specials, ok parking.
Or, if you just need a few things, check out Jeannie at Shop N Drop, who will deliver groceries to your unit, so it will be there when you arrive!