A day out on Tabarca Island is well worth the effort. Sure, the few restuarants are expensive but it's great just to have a wander from one end of the island to the other and then a sit on the beach until it's time to take the boat back.
As for Alicante, why not take a day trip there? There is a bus service from Benidorm to Alicante and you could spend hours there. Stroll around the old town into the Santa Cruz district, take the lift to the castle, walk along the Explanada, explore the area around the Rambla, the marina etc. There's plenty to see and do, loads of bars, cafes and restaurants. You can find a 3 course lunch plus drink from as little as 8 Euros (I know one restaurant that does 4 courses, table salad, bread, half a bottle of wine and coffee for 9 Euros). Try the Plaza Santissima Faz behind the Town Hall, several great restaurants to chose from. Alicante is fantastic city and well worth at least one day of your holiday.