Hi LG:
Between the black flies and the tics be sure to wear some bug spray. Deep Woods Off helps tremendously. And check the dog thoroughly before letting him back in the car! I have put together some info on hiking in the Belknaps which I will post below. If you haven't been up Locke's Hill that is an easy hike with fantastic views. If you have not been up to Belknap Mt. that also is a good take. You drive up a winding road with switchback curves over rushing rivers. If that wasn't excitement enough, then you get to the trailhead! At the top there is a fire tower you can climb. By all means bring your camera and share your photos! There are marked trails at the top that connect to Rowe, Gunstock, Major and Straightback if you are really ambitious.
click here for Belknap Trails
This link has info about trails at Red Hill and Squam Lake
link to Red Hill trail info
Finally, the Lakes Region Conservation Trust maintains many "publicly-accessible" properties including Stondam Island and Five Mile Island. On my "to do" list is Copple Crown in Brookfield/Wolfeboro where I understand there is a fantastic view of the lake.
Stonedam and Copple Crown
Other Lakes Region Conservation Trust Properties
Have fun!

and don't rely on your cell phone if you get in a jam. It may not work up in the mountains!
McD