I'm not sure that you will be able to find a lakefront campsite on the BIG lake. (Although that Long Island Bridge Campground looks pretty nice) This place looks nice...
GREENTOPS CAMPGROUND and has access to the lake with a marina right next door.
There's also
WILEY BROOK CAMPGROUND and
WOLFEBORO CAMPGROUND which look very nice, but are not right on the lake.
If hiking is a priority,
GUNSTOCK would be the place to hang out. Nice sites and all
hiking trails in the Belknaps are accessible from there. Check out the interactive site map. Mountain Biking too! It's not on the lake but
ELLACOYA STATE BEACH is right down the road.
Good Luck!