We stayed near Valtos beach and my favourites were Barbra Nassis, right on Valtos beach towards the harbour end (typically Greek and good value) and Flisvos, near the castle on the track between Valtos and Parga town, with great views of the sunset over Valtos beach and good food.

Try Sakis near the castle, great food and value, To Hani near the harbour, same great food and value and Don Dokis on way out of Parga excellent, theres Stefanos near the castle, Cristos at Sarakiniko beach, Perivoli also gets great write ups and very busy, A weeks not plenty so a few days definitely won't be.

When we went to Parga 2 years ago our fave taverna was Taverna Golfo on the little beach to the left of the town beach. It was family run and you got a big choice of accompaniments with your meal, loads of different veg, rice, boiled, baked, jacket spuds or chips. We get fed up of chips with eveything. They also have a greek night with music several times a week.
I agree with some of the previous posts that there are some good tavernas high overlooking Valtos Beach as well.
At lunch times there was a little fast food place with a bakery attached by the side of the town beach. He did great pita gyros or souvlaki and would wrap it in foil for you to take to the beach. Yummy!
Enjoy

Try Bacchos on the front. Food is delicious and plenty of it. We also liked Filomila (up near the castle) which is a bit more expensive but makes a change from typical Greek food.

HI i went to parga last september and found that there were some lovely tavernas on the harbour. There is a lovely chinese restaurant on one side. Also near the part of the beach where you hire the peddlos there is a gorgeous taverna which serves quality greek and english food as great prices.

You'll really enjoy it there i thought it was a wonderful place.

Stefanos Taverna at the top of the Steps/Slope(whichever way you are going at the time) is brilliant! Fresh (the same day) caught fish which can't be beaten and the other dishes are all good too brilliant views over the bay and a very good "host" (yes I'm biased.. he's my longest standing friend in Parga) but never the less highly recommended by all, Ostria for Italian food is very good too, directly under the castle,on the front, Island Bar & Restaurant is excellent as is Zorba's !