Not really my end of the lake, but I don't remember there being a lot places to buy fuel near Center Harbor. Since you're trailering, why not fill up on land before you launch?
The best place to anchor and picnic around there is what we call Patrician shores. It's in the center of this map
http://www.bing.com/maps/?v=2&cp=r8f...=b&form=LMLTCC
Be careful getting in there it's rocky but well marked out in front.
You are also pretty close to Braun Bay, search this site for more info.