supermarkets are pretty cheap for food and drink, some of them have really nice meat/butchers.
lots of resturants around offering good value for familys as long as you dont go mad, beer and wine and spirits very cheap in supermarkets, you can have a nice tapas meal selection in canarias typicos, we do, around 10 euros each will be about it, pay more in the evenings for steak etc, but, generally good value.
i take a fishing rod and catch my own supper.
fish prices are good if you can get up early and go to market.
frozen fish is cheap too.
lots of resturants offering menu del dia, soup or salad, fish or pork chops with veg, glass of wine, for around 12 euros.
some of the bigger supermarkets offer even better value.

Unfortunately we don't have a foodie market where you can buy fresh fish. However, down at the harbour where the ferry goes to Fuerteventura, there is now a fishmongers open. Stand with your back to the ferry, and you'll see a restaurant right in front of you. Look to the right, and the pescaderia is just there. Big red letters - you can't miss it. The fish is of tremendous quality too. Like SimonWoods said, the frozen fish is good and cheap. Look out for "gallo", which is a good chunky white fish. Spar at Punta Limones sell it, and it's only a couple of euros for 2 fillets.

Supermarkets: Hiperdino is the biggest, and is on the dual carriageway that runs from the harbour to the town centre. Spar isn't bad either - but the one at Punta Limones seems a little cheaper than the one in the town centre.

Plenty of places to eat out at reasonable prices. We generally pay around €15 per head for 2 courses each, and then drink is on top. Brisa Marina is fab, on the seafront. The kids can gawp at the parrots outside, and you can order the best of the menu. I highly recommend their Canarian Stew, fish soup, sole, and steak. All fab!

A new place has just opened in CC Papagayo too - for lunchy stuff. It's run by a German lady friend of ours (don't worry she's fluent in English... and can understand me when I'm drunk, so you'll have no problems). It's called Cafe Aroma and does sandwiches, rolls, jacket potatoes etc etc. There's also beer on draught, plenty of soft drinks - and Ben & Jerry's Ice Cream... hurrah!!

Have a great time!

Elle xx