I think I know what place your probably staying at, near the old Munsonville post office. I’ve stayed in a “school year lease” rental twice on Granite, it’s an awesome lake! I loved it because I’m a big ice fisherman and Granite has lake and rainbow trout. I would put traps out and sit in my living room watching tv.

You have the Monadnock-Sunapee Greenway trail go right by the north end of the lake. Going South takes you into Nelson and eventually Mt Monadnock, North to Washington and eventually Mt Sunapee. There’s a guide you can probably find at Toadstool books in Keene or Peterborough

I second Willard Pond, and bald mountain next to it. Also Mt Skatutakee and the Harris Center trails in Hancock. Pitcher Mt is cool, you could actually walk there and back right from your door on the Greenway, with a waterfall on the way.

I recommend this book, it’s about a hermit that lived off the end of Aten Rd on the back side of the lake