Mt Agamenticus is up around York so may be a little more than 30 minutes from Exeter, but it’s got a handful of different loops so you can choose different distances and the peak has gorgeous viewing platforms of the ocean and the looking inland at the other mountains. If you go during berry season there are ripe blueberries, blackberries and raspberries all over. I used to live in Portsmouth and it was one of my favorite morning hikes.