Staying in Palm Cove with teenagers (who eat !) is a very costly exercise. The restaurants at Palm Cove are NOT family friendly when it comes to prices and unless you have lots of spending money, you will soon run out.
A five minute drive towards Cairns however, will bring you to the Clifton Village Shopping Centre. Nothing flash, but it has everything you need - including good coffee shops, a large supermarket and at least three good restaurants.
Located at Clifton Village is a great family run Italian restaurant - A Taste of Italy. The food is all freshly cooked and offers a range of pizza, pasta, chicken and meat dishes. Unlike Palm Cove, the prices here are VERY family friendly - with dinner (three courses) for 4, including a modest tip, costing only $74. It's BYO and there is a wine shop at the centre. Plenty of free parking and you can sit outside if you wish.
We had a young German backpacker as our waitress and she was very friendly and efficient. The very pleasant owner (who also does some of the cooking ) visited us a couple of times to make sure we were happy with the food and said she'd hope to see us again one day. She will !
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.