So many choices.
You may want to consider parking at the terminus of the Northville-Lake Placid Trail (off Avery Road) and hike down the N-LP trail. About 6+ miles in you come upon Wanika Falls. This is a great place to visit. The falls drops over a series of rock outcroppings hunders of feet.
Beyond that about another 1.5 miles you come upon Moose Pond lean-to. This is a very scenic sight, plenty of room and not much traffic.
The trail in you come upon beaver dams, which has good educational value and is relatively flat. Should you go anothe 3.9 miles, you come upon Duck Hole which is one of the best areas in the ADKs. It is worth seeing before the damn breaks and empties the lake. If you hike in the ADKs this is one trip everyone should make.
You can see some pictures,
here.
and a trip repoert,
here.
Good luck on your trip.