Telegraph Cove is an awesome little community, and it does have marine gas to fuel the boat. I have stayed there in the past and have liked the location. Although, to my mind the condo development has somewhat taken away from it's rustic charm. As it is easily accessible by paved road these days I would personally look for a port that is more off the beaten path to overnight. Murph is right Telegraph Cove is a cool place to visit, but you can easily go there if you are visiting the north island with a vehicle. If I were doing that kind of trip by boat, I think I would want to stop at a few places that I might never get to see without a boat. That's just my perspective, but I've already spent a fair bit of time in that area. I'd rather stop at a few places that I might never get to see without a large boat at my personal disposal.
I'm sorry, I don't have any alternative suggestions. Perhaps others could give you some ideas, or maybe pick up a copy of a cruising guide that might give you some ideas. I'd suggest contacting any location you're considering staying at by phone first. Gas barge hours and moorage availability can change with little notice, and you don't want to be surprised if you arrive without prior contact. Best to make reservations in advance, especially if traveling around the August long weekend. A good current cruising guide should list all the marina phone numbers and their hailing channels on the VHF radio.
Good luck, and good fishing. That sounds like a bucket list trip for sure.