How about Johnny Napkins on Rt. 22 West in Springfield? It's in the Hotel 304 West (used to be the Holiday Inn). Good contemporary American bistro food like burgers, wraps, salads and pizzas. (I'm a big fan of the port wine cheeseburger..) Funky drinks too.
Dylan's in Mountainside (Mountain Ave. I think) has good food but I can't comment on how low key it is during the day.
If all else fails and you do want to do the diner thing, hit the Scotchwood on 22 East in Scotch Plains.