You picked the wrong side of the lake for hiking
Red Hill is the only thing nearby that I can think of. I don't think there are any hiking trails in the Ossipee range. Squam range has Morgan, Percival, and Rattlesnake which may be your best bets but that is indeed a haul. And of course going clockwise around the lake gets you to the Belknap area. Not a great location for nearby hiking.