For today's Snapshot, we're actually just heading to the next town over from New Providence, where we saw the ACME yesterday. This store, at 21 Summit Ave, is a 1950s-era or earlier store that was a supermarket until the 1980s or 90s.
The entrance and parking lot are located in the back of the store. As of the time of photography (June 2018), the store was still using A&P's Best Cellars branding. The independent owner may have purchased the name from A&P.
The store, as shown in Dan Asnis' 2012 photo over on Flickr. A&P actually renovated the facade, not the new owner.