The Griswold is OK for cocktails, but for food you are likely better off elsewhere. Yacht facilities are all close to town - easy walking distance - Essex Boatworks, Essex Island Marina, are north of the main street, The Essex Corinthian Yacht Club and Essex Yacht Club are on the south side. Some only seem to have slips, so can be pricey. The menu at Essex Yacht Club is very good. Otherwise, gourmet restaurants (Bee & Thistle Inn, Restaurant L&E, River Tavern) are a cab ride away. If you have a dinghy, try a visit to Gilette's castle, up the river a bit, and don't miss Hamburg Cove.
Essex Yacht club moorings are less expensive than a slip at Essex Island Marina. One disadvantage is that the launch stops pretty early on weekdays, so if you are going out to dinner, you might be better off leaving a dinghy at the dock to get back. The Griswold is not to be missed, and I've had several decent meals there over the years.
If you've never anchored at Duck Island, we aware that the current there is strong and depending on wind, can cause the rode to wrap around the keel. I set two anchors there to avoid that. Note that Westbrook is right there and the Brewers marina is excellent and its a relatively short walk to Bill's for real New England shore seafood.