I've never actually eaten in the City of Downey, but there's good stuff nearby: there's fish and shrimp tacos from El Taco Nazo (several locations in the southeast 562), steaks, chops and a healthy dose of a bygone era at the Dal Rae in Pico Rivera, Burmese food at Golden Triangle in Whittier, La Huasteca for "alta cocina" Mexican food in Lynwood, and if it ever reopens, Renu Nakorn, one of the premier Thai restaurants in the US, in Norwalk.
Agree with Das Ubergeek's recs and might add Casa Gamino for every day Mexican food in Pico Rivera on Slauson or the location in Paramount, whichever might be closer. Not the world beater, yet gives El Torito/Acapulco etal some good competition.
The Amapola market at 7414 Florence, Old River School cross street I believe, is a good grocery store with a very tasty deli section. Used to have restaurant but closed it - too bad, it was quite good.
Stox at 9518 Imperial Hwy is not bad for American comfort food, yet don't go thinking it will challenge any gourmet restaurants, but is fairly reliable. Some of the waitresses are a hoot, and the bar is home to some of Downey's oldest residents!!!
Not sure of the name, but you have an excellent Cuban bakery off of Florence and Downey I believe. Great deserts, have a friend that always goes there and brings something for get togethers.
Jusagthing's suggestion regarding the Cuban bakery was right on. It's delicious. The Cuban sandwiches are excellent, but not the best I've ever had. Still, they do hit the spot. I believe it's called "Havana Something". It can be hard to spot--it's right next to the corner on Paramount at Florence, small building with a small blue sign. Buy anything sweet there and you will enjoy it. Friendly employees, great atmosphere.
There is a great little Chinese restuarant on Downey Ave. called "Peking Palace", I think. It's the only Chinese place on the block. Delicious Chinese food. I would eat their hot & sour soup every day if I could. Their seafood soup is also terrific and spicy. I get hungry just thinking about it. It's open 'til nine and closed on Mondays. It's nearly always crowded, so expect a wait in the evenings around dinnertime. I can't say enough good things about this place.
Across the street from that is an Italian place--I forget the name of it, but it's been there for 14,000 years and they have karaoke during the week. Very friendly place, cute decor, not the best Italian ever, but still very good and a great alternative to the Olive Garden at the mall (which is ALWAYS packed and tastes bad, besides). It was very lively when we went and packed with friendly, tipsy regulars... might've changed a bit but I know that place is still there.
There is a tiny little place called The City Deli on Downey Ave. I don't know if they're still there, but when they were, they delivered large, very tasty egg salad and chicken salad sandwiches. Perfect for a day when you're too busy to cook. Check to see if they deliver to your area.
There is a Cuban restuarant/bakery on the corner of Old River School Road and Firestone. It has a much more extensive menu but less bakery items than the other place. It's good, but I was not overly impressed with it. It's nice if you want something different and don't want to drive too far.
Pina Pizza House on Paramount is not bad. A good alternative to Pizza Hut and Domino's. Big menu, inexpensive. Order out rather than eat in--the ambience is a little chowhall-ish.
Last, but certainly NOT least, is a taco stand on Firestone, across from Home Depot. Talk about always packed! Raul's Tacos is your typical greasy, cheap tacos al carbon stand. Not to everyone's taste, of course, but there's something about their carne asada tacos that does it for me. They're open every day, and until one or two am on Fridays and Saturdays. If you're there on a Friday or Saturday, ask them for cebollitas with your order, and they'll give you a little tinfoil packet of quartered and grilled sweet onions for free. Beware: their burritos and tortas are absolute monsters.