We've been working in a similar space (hyperlocal for furniture, home decor and fashion) for about 5 years with ATTIC (https://attic.city). The premise of our work runs a bit contrary and challenges a platform like this -- the primary issue is store willingness to participate in yet another platform.
Putting grocery stores aside, most other retail stores have too much to do and manage on the tech/marketing front: facebook, instagram, twitter, pinterest, snapchat etc. Add on their own website with its own e-commerce platform plus several other shopping or delivery platforms (etsy, posh etc) -- it's too much. As a result we've ended up with extremely fragmented marketplaces and none do a good job of showing a comprehensive view of your local shopping options. For example, some restaurants I like are on X. Others are on Y. Others still are on Z.
Like I said, we came at this problem from a different angle. We're indexing local stores to build the platform that actually has a comprehensive view of a local market -- and to fill in the gap that services like Google Shopping do a poor job of representing. It's slightly slower out of the gate as we do some preliminary research for each city/market. But we've launched ATTIC in 9 major US markets so far and expect to be at 15 by year's end.
As an aside, do you know where you first came across the term hyperlocal? I wonder who coined it. We've been using it as well, but we're certainly not the first.