I second Ecco on Rt. 18 in Weymouth for both atmosphere and very good food- it's the best value around.
Maria's is an old Italian/Greek red sauce joint on 53 in Braintree.
Fuji in Quincy Center has the best Sushi on the South Shore.
Down the street from there is Fat Cat- gastropub type of stuff. Small and always crowded
For Thai- head to Randolph for Malai. The service is very friendly, if slow, and the food is great and the atmosphere is better than most Thai places.
If you just want something for take-out, Tennessee BBQ is a good bet for pulled pork and Mac and Cheese.
There's Nino's on Rt. 53 in Hingham which offers a decent value for steak- much cheaper than Scarlet Oak further down the road but the quality is also less.
I'm also a big fan of El Sarape. Great margaritas and good mexican food.
Great suggestions already, and I'll add Punjab Cafe in Quincy, not far from the Weymouth line. It is in an unlikely location in a strip mall on route 3A across from a CVS, but the atmosphere, service and food are very good value. I really like their breads.
If you can get there M-F Punjab Cafe and Little Q have well-priced lunch specials, and
Punjab Cafe has a well priced weekend buffet brunch.
Grumpy White's Restaurant
211 Sea St, Quincy, MA 02169
Little Q Hotpot Restaurant
1585 Hancock St, Quincy, MA 02169
653 Southern, Artery Quincy, MA
Are you looking for nice atmosphere too, or just good cheap food? If you like Lebanese food, Webster's (in the Pilgrim Place strip mall off of Quincy Ave.) has excellent food, especially the shish kebabs. It's sit down and waitress service, but the ambiance is more like sub shop than anything else, so go for the food.
I also love Grumpy White's, which is on Sea St. near Houghs Neck in Quincy. It's classic American food like hamburgers and meatloaf and it's dirt cheap and very good.
El Sarape in East Braintree/Weymouth Landing has good Mexican food, and the prices fairly reasonable. Other than that, I'd say go next door to Quincy or Weymouth, where there are several options (for example, Little Q, Gennaro's, and Quincy Dynasty in Quincy; Ecco and Sweet Lemons in Weymouth).