When: Summer for nice weather, fall to avoid the crowds
Where: Acadia National Park is located 5 hours from Boston. The main park area is within miles of Bar Harbor, ME
Why: Acadia is the most dog-friendly National Park. There are over 100 miles of dog friendly trails. Many restaurants and inns in Bar Harbor are dog friendly. If you don't have a pup, Acadia is well known for its coastal location. Most of the hikes are moderate, so it makes for a good relaxing hiking trip.
5PM: Leave Boston after work and make the long drive up to Acadia. There are rest stops along 95, but the food isn't so interesting (Think Burger King, not even a McDonald's!). If you're looking for something quick, think of packing your food or stopping by the Chipotle/Panera Bread in Augusta. Otherwise, Portland ME is a great option for Thai take out.
10PM: Check into Blackwoods Campground, one of the 2 dog friendly campgrounds in Acadia. You need to make reservations in advance, but you do not need to inform them that you will be checking in late. Find your name on the sheet when you arrive and drive to your designated spot.
5AM: Wake up bright and early to catch the sunrise along Ocean Path. You can either drive to Otter Cliff and work up to Sand Beach, or park at Sand Beach and walk south to Otter Cliff. Most photographers will camp out at Otter Cliff. You can find the sunrise time at Acadia using this website. There are multiple stops along the nice 2 mile Ocean Path including the infamous Thunder Hole. The best time to catch Thunder Hole is 2 hours before high tide, or during rough ocean conditions.
9AM: Head to Bar Harbor for breakfast. 2 Cats is excellent, but be prepared to wait anywhere from 30 min - 1.5 hours. While you're in town, check out Bark Harbor.
11AM: Now that you're all filled up, head to the middle of the island to Acadia Mountain. Standing at 681 feet, it is a modest mountain with spectacular views of the ocean. The total hike can range from anywhere to 2-4 miles, depending on which route you take. The rock scrambling is not bad, but I would still recommend hiking shoes instead of sneakers for the descent. The trail is nestled amongst spruce and cedar trees, and there is descent coverage for most of the ascent.
3PM: Head back to your campground and relax. Maybe make a snack.
6PM: Drive to the quiet west side of Mount Desert Island to Seal Cove. It is one of the most spectacular coastal sunset spots you will see in New England. There is ample street parking.
3AM: If the conditions are right, head up the Cadillac South Ridge Trail for the infamous Cadillac Sunrise Hike. Note that like Mount Washington, cars can drive up Cadillac Mountain. You might experience some shock when you move from complete darkness and solitude to a mob of tourists at the summit. Cadillac Mountain sees the first sunrise in the fall and winter.
9AM: Pack up and head home!
I purposefully haven't included much detailed hiking information because there are a lot of great resources out there. Joe runs a great site that gives you more details on the hikes I've mentioned here.
TripAdvisor, Lonely Planet, and Yelp are also good resources for lodging and food.