Take the Island Explorer Shuttle from the Village Green, right in downtown Bar Harbor. Route 3 (Sand Beach) will take you to Otter Cliff & Sand Beach, which have some great day hike options. We love the Beehive Trail (moderate) or if you have some extra time to spare, Precipice Trail (difficult)
Grab an ice cream cone (fresh blueberry softserve from CJ's Big Dipper) and walk around downtown Bar Harbor.