Some ideas

Greenwich has a relatively poor food scene for a town of 60,000 and only 35 miles from NYC. But if you are in town and need places, here are a few:

Little Pub in Cos Cob, good pub fare/burgers.

Fat Poodle in Old Greenwich is a go to for decent date night dinner.

Applausi is serviceable Italian I’m Old Greenwich. Valbella, near your hotel is overpriced red sauce but odds are you will run into Regis and Joy.

If you have a car, The Whelk in Westport is great, as is the Tavern at Silver Barns in Norwalk.

I’d second the idea of driving up to Zuppardi’s (get the sausage pie special) in West Haven or Sally’s in New Haven for a pie. Best pizza ever.