I'm sure others will chime in with places you don't have to drive, but if you can spare 5 miles/10 minutes, I really, really, REALLY like Saybrook Soup & Sandwich Co.
More reviews here:
In Essex itself, there's Olive Oyls. I haven't been in a LONG time, but don't think there's anywhere for you to sit and eat. Someone who's been more recently can tell you better.
Olive Oyls is reliable, if its a nice day you can picnic up the street near the gazebo, there are picnic tables. In Essex downtown other than the Black Seal & The Gris there's not much else.
Centerbrook, only a few miles away has Bennies which is a market and also does some great sandwiches and the Centerbrook Cheese Shop (my new favorite) has meats, cheese, of course, and breads. There is also Pizza Pub in Centerbrook. IMHO it's ok, but given the other choices......