I feel really bad as a Capetonian that there's rarely responses to Cape Town based questions on this board, so here are my current favourites. Please note this is based on where I, as a local, choose to eat, which is rarely the expensive nouvelle cuisine places in the Winelands or the centre of town, which I frankly find all sort of the same and boring.
A seaside institution. Still has great atmosphere, view of the fishing boats in Kalkbay Harbour, and I think a really fresh menu, which changes daily. They get the fish straight off the boats. No reservations, so come early or wait in line. Otherwise you could try Live Bait on the harbour wall, or Kalkies, also on the harbour, for fried fish and chips like the locals enjoy.
The cheapest sit-down Indian food in Cape Town. Very popular with Muslim families from the Bo-Kaap, or after Mosque. Darling Street, opposite the post office. There's no sign, just an open archway. No frills, but cheerful atmosphere. Grab a falooda (Cape Malay pink milkshake) and choose from curry of the day, dosas, tandoor, etc. Potato pakoras rock. Mainly Indian, with a little bit of confused (don't get the chinese food or shwarma!) and Malay thrown in for good measure.
Affected nightclubby atmosphere, but the best Chinese food in Cape Town, bar none.
Bar salon on Bree Street. Trendy, fun decor and umbrellas outside on the square. Menu is very meat-centric (sausage, anyone?) but a good place to get a traditional boerewors roll and a beer.
A strictly daytime kiosk overlooking the street with benches for those so inclined, the bakery attached to the restaurant of the same name makes seriously good bread, and seriously good sandwiches. Grab some on the way to Campsbay or Clifton or the Table Mountain cable car for a picnic. Bloem Street, off Long.
Get yr hotel to organise transport to this one, a mainly open air braai joint in the townships. very good meat, township vibe, and everyone's friendly. Leave the vegetarians at home.
BISCUIT MILL NEIGHBOUR GOODS MARKET
Saturdays, 9-2pm. Food market. Can get quite crowded, but has the greatest concentration of seriously good food in one area in all of Cape Town. People say it's expensive and precious, and it is that, but on a food level, it offers a wonderful selection of local and international foods, and lots of new and quirky food ideas. There's a sister design and clothing market next door, for those inclined to see some local design (Heartworks store in the complex also offers great locallymade gifts and mementos).
Massimo's Pizza Club (pizzaclub.co.za)
Only open Wednesday through Saturday nights, on the main road into Hout Bay, offers the best pizzas in Cape Town with unique concept - all the pizzas are passed around and shared by all diners.
If you're going to the Winelands (and please don't - it's so full of tourists during high season that I avoid it!), French Connection does genuinely good, simple food (so if you're looking for gastrique this and garnished that, you'll be disappointed) on the Franschhoek main drag. My parents were at Solms Delta yesterday, and said lunch was unaffected and charming (and there's a great slavery and apartheid mini-museum there, for history buffs). Reubens has great service and the food's good. Le Quartier's tasting menu is legendary, but it takes about four hours and is a bit fiddly (I've done it once, enjoyed it, but prob wouldn't do it again). Bread and Wine at Moreson is probably my favourite, with food that's sophisticated and simple, for all tastes (you don't need a reservation to sit at the charcuterie bar in the deli and have things like bacon-and-butter sandwiches, which is as good as it sounds).