You will love Grand Case!
We typically grocery shop at Simply in Hope Estate, which is about 5-10 mins from GC. There is wine/beer/liquor there, but pretty sure there is also a store next to it as well. We have also stopped at Le Grand Marche on the way from the airport to GC for more "American-type" grocery options.
We enjoy wine with dinner as well, and a cab to maho area is about $30 each way. Not sure about live music options on the Dutch side, but Calmos Cafe in GC has live music on Thursday & Sunday I think. You can prob dance at Tantra in maho, but we typically crash after dinner wink
You can either take the ferry over to Anguilla & explore for yourself (leaves out of Marigot), or Creole Watersports offers a trip over as well (they operate out of the Grand Case Beach Club) Scoobi-Too also offers trips out of GCBC.
As foodies, we highly recommend Piazza Pascal & Le Pressoir & L'Auberge Gourmande. Sunset Cafe at GCBC also has great food & a great view. In Maho, we love Le Moulin Fou. Enjoy!!