Different restaurants to different things well in Camogli, and you don't state a budget to it is hard to advice.
All around, and in the top range, Nonna Nina is worth the trip up the hill. You need to take a bus up, but you can walk down, even at night. The stairs are well lit (if you have no mobility problems).
Rosa's has one of the best lasagne al pesto around. It's fried fish (fritto misto) is good. Skip antipasti.
Da Paolo makes a memorable cuttlefish (seppie) pate and excellent seafood risotto. Otherwise, skip it.
It is worth going out of town to Chiavari to eat farinata at Luchin, to Rapallo to have gelato at Frigidarium (on the seaside, opposite the castle) and to either Recco or Nervi to sample foccacia al formaggio. (In Recco, Moltedo is the best, take-away only, or you can sit down at Manuelina, a hike from the train or bus station; in Nervi, La Marinella is on the seaside promenade, the Passeggiata Garibaldi).
Also worthwhile in Camogli for a light lunch is Le Creperie, which isn't italian but the food is very fresh and the view is exquisitely charming. The enoteca I Tre Merli has the best local red wine (rossese) and the enoteca Bossa on the via della Republica has some of the best fried anchovies in the area. On the same street, the tiny hole in the wall bar Il Bricco has the town's best cup of coffee.
Via Roma, 296, Recco, Liguria , IT
via Bighetti, 41, Chiavari, Liguria 16043, IT