One of the best full day trips is to Mohegan Island.  You will need to book a trip on Hardy Boats out of New Harbor (about 30 minutes away).  The boat ride is about an hour.  Leave on the 9AM and come back on a 3:15PM ferry.  You might want to avoid very windy days, as the ride can be rough.  Also, it is typically 5-10 degrees cooler on the island with wind.

Take a backpack with water.  You can bring a lunch or buy a lunch and snacks at the store once you land on Monhegan.  You can also buy a trail map (there is a screenshot below - we usually go left).  Definitely get to the back cliffs - that is where we usually stop for our picnic after a couple of hours of hiking.

Keep hiking and by around 2, try to wind up at the Mohegan Brewing for a beer before walking back about 10-15 minutes to the ferry.