Winemark's right--the Lyceum is a good bet for something nice but not too too fancy.
You can't get much more local than Red's Sandwich Shop on Central St. They serve breakfast and lunch (cash only) and the food's good, in an all-day-breakfast greasy spoon kind of way.
The corned beef hash is homemade, the pancakes are (literally) the size of dinner plates, and the cups of coffee are bottomless. The people watching is entertaining, too, since Red's is patronized by everybody from firemen to goth kids to grandmas.
Don't be afraid of the line in the morning--it moves fast.
Mc Swiggans on Essex across from the Hawthorne Hotel has good pub food and some well-executed more ambitious seafood and pasta dishes.
Asahi in the Essex St. Mall has decent (though not destination) Japanese/sushi.
In a Pig's Eye on Derby St is good for Sunday brunch. It's a neighborhood bar/restaurant, with good variations on eggs benedict.
Cilantro, also on Derby, has interesting and pretty authentic Mexican. I find the prices a bit high, though, so I usually eat at their takeout window around the corner--A Taste of Cilantro. It has tacos, burritos, and several Mexican stews on the menu at much lower prices than the mother ship.